Moatsos, Ioannis (2005) Ultimate strength of ship structures ...

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Moatsos, Ioannis (2005) Ultimate strength of ship structures including thermal and corrosion effects: a time variant reliability based approach. PhD thesis. http://theses.gla.ac.uk/5326/ Copyright and moral rights for this thesis are retained by the author A copy can be downloaded for personal non-commercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given.

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http://theses.gla.ac.uk/5326/

ULTIMATE STRENGTH OF SHIP STRUCTURES

INCLUDING THERMAL AND CORROSION EFFECTS:

, A TIME VARIANT RELIABILITY BASED APPROACH

By

Ioannis Moatsos MEng (Hans)

Thesis submitted for the Degree of Doctor of Philosophy

UNIVERSITYof

GLASGOW

Department of Naval Architecture and Marine Engineering

Universities of Glasgow and Strathclyde

The 1st of December 2005

© Ioannis Moatsos 2005

For my cousin Nicolaos Metaxas

& all the family members I lost during the years of my studies .

I wish I could share with them what I have achieved today .

The places I've travelled, the joys I have lived,

my plans for the future, my dreams being fulfilled ...

May the Lord allow them to watch over our family,

Whenever we may sail, compete or travel by sea ...

Eternal Father, strong to save

Whose arm hath bound the restless wave.

Who bidd'st the mighty ocean deep

Its own appointed limits keep

Oh hear us when we cry to thee

For those in peril on the sea

Rev. William Whiting. 1860

ABSTRACT

The aim of this Thesis is to investigate the effects of temperature variation, slamming and

corrosion on ultimate strength in a structural reliability context. Ship structural design has

traditionally been driven by rule-based deterministic procedures. Assumptions are made that

all factors influencing the load applied to that structure are known and that the strength-load

effects are a known function of these parameters, ignoring uncertainties that might occur

such as fluctuations of loads, variability of material properties or uncertainty in analysis

models, all of which could contribute to the possibility that the structure will not perform as

it was originally designed. High implied margins of safety or load factors generate

structures that are on average appreciably stronger than their nominal as-designed ultimate

capacity. Structural reliability analysis offers an alternative stochastic structural design

process based on probability theory where a structure can be designed with adequate and

consistent level of safety.

InDecember 17th 2002 the World Meteorological Organization issued a statement according

to which the global mean surface temperature has risen and consequently 2002 was the

warmest year in the 1961-2002 period. Positive sea surface temperature anomalies across

much of the land and sea surface of the globe in general contributed to the near record

temperature ranking for the year along with climate anomalies in many regions across the

globe. Climate change as a result of global warming is a worldwide occurring phenomenon

which the experts have only recently started to understand and which affects and

significantly will affect us in the near future. The effects of climate change have been

somehow neglected by the ship and offshore related academic and research communities.

In the case of thermal effects on ships structures, unless the problem solved is temperature

dependent, this type of stress has often been neglected and not been taken into account in

most types of analysis. The most likely reason behind this would seem to be that the stresses

produced from temperature changes would be too small to be taken into account compared

with still water loads or wave bending stresses. This is not the case though. Records exist of

ships having broken in half while moored in still water and major hull fractures occurred in

still water while the temperature was changing as it can be seen from the relevant published

literature. Very little work on thermal stress on ship structures has been published since the

1950s and 1960s and no work has been done that considers temperature effects on ultimate

strength.

Research undertaken aims to incorporate temperature effects on existing ultimate strength

formulation by using a thermal stress approach, compare and use recently proposed

corrosion models to model corrosion effects on ultimate strength and provide a foundation

on which reliability analysis could then be performed for TankerIFPSO structures operating

in the North Sea. After comparing a number of possible approaches that would enable the

loading components to be combined in a stochastic fashion, the loading part of the

reliability analysis is handled using extreme wave statistics and the Ferry Borges-Castanheta

load combination method. Annual reliability indices and probabilities of failure are

calculated for hogging and sagging conditions using both time-variant and time-invariant

approaches and a variety of reliability analysis approaches showing the effects of

temperature along with Partial Safety Factors for all variables taken into account.

DECLARATION

Except where reference is made to the work of others,

This Thesis is believed to be original.

ACKNOWLEDGMENTS

The author would like to express his sincerest gratitude to his supervisor, Prof. Pumendu K.

Das Professor of Marine Structures in the Dept. of Naval Architecture and Marine Eng. of

the Universities of Glasgow and Strathclyde for all his guidance, valuable assistance,

support, encouragement and technical excellence that made possible the successful

completion of the present work.

The author would also like to express his sincerest gratitude to the Alexander S. Onassis

Public Benefit Foundation, in Greece for awarding the author with a Doctoral Scholarship

allowing him to pursue postgraduate studies. Also to the Dept. of Naval Architecture and

Marine Eng., the University of Glasgow, the University of Strathclyde, the UK Health and

Safety Executive (HSE) and the UK Engineering and Physical Sciences Research Council

(EPSRC), The Royal Society of Edinburgh and The Royal Academy of Engineering for

their financial support in the form of Doctoral Scholarships/Studentships that made possible

the funding of this research but also enabled the author's attendance to conferences

worldwide.

The author would furthermore like to express his sincerest gratitude to Mrs Thelma Will,

Secretary in the Department of Naval Architecture and Marine Engineering of the

Universities of Glasgow and Strathclyde for all her help, support and encouraging words

throughout the 9 years that I have been studying in Glasgow. She has a very special place in

my heart.

The author is also deeply and truly grateful to his family for their love, support and

guidance by all means. My mother Irini and my father Rev. Georgios-Nikolaos have always

taught me to follow my dreams and my heart and have always encouraged me to do the

things that I believed and knew that would make me happy. For teaching me above all to

love, to forgive and to always believe in people I will forever be grateful to them.

Through the duration of this degree I achieved goals, personal and academic, and

experienced places, physically and mentally, that if somebody had asked me 10 years ago

whether I thought I would ever achieve, I would have called them crazy. lowe my life, my

work, my success and my experiences to all the people mentioned above equally and for this

I will forever be grateful to them. Thank you ever so much for helping me be the person that

I am today.

CONTENTS

ABSTRACT .•.•••••••••••.....••••.••..••••••••.•...•••.....••...••.••.•.•••••.••..••.•.•...•....•.•••.....•••••••....•••.•••..••••....•••..•.•...•....••••...• 3DECLARATION .•..•••..•...•....••.•.•••.•••••.••...••.••.•.....••••...•.••••••••...•..•.•••••..•..•..•••••.•.••.•.••••...••..•.••.••.•.•..•••••....•.•.••. 5ACKNOWLEDGMENTS .••..•.•...•••••••..•••..•.••••..•....••.•••••..•.•••..•...•••...•••••..•..••..••.....••...••.....•..............•............. 6CONTENTS •.....••••••••.....••••.•••..••••••.•...•...•••..••...•...............•••....••.....•....•.....................•....•..•..•••••.......••......••...• 7THESIS LAYOUT .•••••••.••.•.•.••••.•••..•••.••••..••••••••.•.••••..••••.••••••.••...•.•....•.••..••.•..•.•..••.••.•••...•.•••...•..•.•.•..•.•.••..•..• 11SUMMARY ••••.••.•.....••••••••.••..•...•.••...•.••••.••.••...••••.... :•••••.••...•.•••....•••.••.•••..•.••••...••.•..•...••...••••••••••.••..••.........•• 12LIST OF FIGURES BY CHAPTER •...••....•..••••.•...••.•......•••.•....•......••...•••••.••.••.•..•••...•••..••••...•••••••....•••••..••...• 15LIST OF TABLES BY CHAPTER ..•••....•....•••...•••.•••••••.........................•...•......•..•...•....•...•.........•........•....•.... 20LIST OF TABLES BY CHAPTER .•.•..••........•••..........••••........•...........•...............••.•.•..•.....••••.•••.••••.••••••..•..•..• 20NOTATION-NOMENCLATURE AND ABBREVIATIONS .•••..•••....•.....••..•.•..•.•.•••.•.••.•.....••..•..•..•.•..•••••.•• 22

CHAPTER!

INTR 0 DUCTI 0 N 37

1.1 INTRODUCTION .••••........•..•.•••....•..•..•••••..••.•..•••••.•.•..•.••...•••.•.••.....••••••••••••.•...•••••••••.......•••••....••••••.•..• 371.2 RATIONALLy-BASED STRUCTURAL DESIGN ......•...........•••••..•......••....•...••....••.....•....•.......•••......••••.•. 371.3 RELIABILITY BASED CODE FORMATS .••..••..••..•..•.••••...••••.••.••••••.••••••..••...•.•••••••.•••••.••••••••....••••.•.•.•.•• 391.3.1 CSA OFFSHORE STRUCTURES CODE ......•.••..••••.......•••....•.•...•••••••••........••••.••••...••....••••..••••..••.•.•.•••..• 411.3.2 NORSOKSTANDARDS ••.••..•••••••.•••...••••..•••.•••..•.••••.•.••.•...•.•..••..••.•••.•••....••...•••...••.•.••.••••••••.••.•••...•••. 431.3.3 JCSS PROBABILISTIC MODEL CODE ...••....•.•.•........................••..•.......••........•......••..•............•..••.•.•.. .451.3.4 BV RULES FOR THE CLASSIFICATION OF SHIPS ..•••.••.•....•••...•••••........•••.•.••....•..••.•...•.•..••.....••.•.•.•••.• .461.4 DISCUSSION-REMARKS •..••••.••••.•.••••...•...••.•........•.••...•...•••..•.••••..•.••.•••••....••.....•••.•.•........•.••.••..••..••.•. 48CHAPTER 1,REFERENCES: .••.•.•...••...•••..••••..••••..••••.••..• :.••........•....•.•.••....•....••••....•.....•••.•..•.•••••.•••..•...•••••.•....•.. 50ApPENDIX 1,FIGURES ••••••.•••••..••...••.•.•.•.•.••.••.•••...••....••••••••••••••••....••..••...•.••.••.•.•..••....•••....•...•.••••.•.•....••••..•...• 52ApPENDIX 1,TABLES .•.......•.......•...••.••.•••.•......•......•....•....•.•••....•..•..••.•.•..•..•••.•.•..•.••.•.•••..••••........••••......•••.••.•. 54

CHAPTER2

GLOBAL WARMING AND THE CLIMATE CHANGE PROBLEM ••••••••••••••••••••••••••••••••••••••••••••••••••••••57

2.1 INTRODUCTION •..••..•••..••••..••..•••..•..••...••..•...•••••.••.•.•.•..•.••..••......•••••..••.....••••.••...••.••...•........•.••.••..•••.• 572.2 GLOBAL WARMING & STATEMENTS ON FuTURE CLIMATE .••••••.••••••.•..••.••••.....•••••..•••••••••..•••.•••....•. 572.3 CLIMATE CHANGE RESEARCH IN OTHER ENGINEERING FIELDS....••.•.•...••••..•••..•••..•..•..•••.••.....•.••••..... 592.4 CLIMATE CHANGE CURRENT PROJECTIONS AND IMPLICATIONS, ••..•....•....••••.•.•.••..•.•.....•.••..••....•••••.•. 602.5 THE CORROSION PROBLEM ...••...••...•.••••..•••...•.••••.....••...•••..••..••.•.•.••.••••••••..•...••.•.••.•••••••.•.•••••...•..••.•. 612.6 THERMAL STRESSES RELATED FAILURES IN SHIPS ......••.•••....•••••..•.••••••••••••..••••••••.••.••••.•••••.••••.•••..•.•. 632.7 ApPROACH TO BE FOLLOWED .•••.....•..•.•..••••••••••..•••••...••••...••.••••.•••••..•....••••..••••.••..•....•..••••....•.•••.••.... 65CHAPTER 2, REFERENCES: ...•••.••••.••••.•••..•.••..••....••••...•.•••.•••....•••..••...•••.•••..•.•...••........•.••••.••••••••..•.•.•..••...••••..•• 68ApPENDIX 2, FIGURES •...••.•.••..•.••..•••.•.••...••••...•••••••.....••...••••..••.•.•.•....•.•••..•...•....••..•.•••.......••••••••.....•••.•...••••.•. 70

CHAPTER3

CRITICAL REVIEW OF PUBLISHED WORK •••••••••••••••••••••••••••••••••••••••••••••••••••••••••.••••••••••••••••••••••••••••••••73

3.1 INTRODUCTION .••.•.••••..•••...•••.••.•••••..••••.•••.••••••••••••••..•••.••..•.•••..•••••••...•..••....•.•••••..•••••••••...•••..•.....•••..•.••...•. 733.2 THERMAL STRESS ON SHIP STRUCTURES PUBLISHED RESEARCH 733.2.1 INTRODUCTION ••••••.••••••.•••••..••••.•••••..•••..•••..••.•..•••....•••••.••••..•..•••••.•••••••.•...••••••...••.••..••••••••.••...•.••••..• 733.2.2 DEFLECTION .•••••.•••....••.•••.•••..•••.•.••••.••••...••••.........•••.•••...•••.•••..••••...•••••••...••••••....••••.••.•.•••..•..•...•••..•• 753.2.3 CHANGES IN PROPERTIES OF MATERIAL •.••••••••.•.•••••..•.••.•••...•••••..•••.•...••••..••••....••••••..••••••....•••.•.•••..• 753.2.4 TEMPERATURE STRESSES .••...••••••••..•.•.•..•••..•••••.••.....•.•..•••.•......•.•..•..•....•.•..•••...••..••.••••..••••..•.•...•....•. 763.2.5 CALCULATION OF TEMPERATURE GRADIENTS AND THERMAL STRESSES - THEORETICAL ANDEXPERIMENTAL .••....•..•••••••..••••••.•.••..••....•.•••••••••••••••••••••...••.••••.••••.•••.•.•..•••••..••••..•...•••.••••••.•..•...•••.•••.••....••••.•. 763.3 ULTIMATE STRENGTH OF SHIP STRUCTURES PUBLISHED RESEARCH 783.3.1 INTRODUCTION •..•••••.••••...••••.••••••.•.••.••••.•.••.•.•••.••••..•.••...•..•..•.•.••...•.•.•....••...••....••.•.••.•..•.•••••.•.•••••••••• 783.3.2 STIFFENED AND UNSTIFFENED PLATE ULTIMATE STRENGTH 793.3.3 HULL GIRDER ULTIMATESTRENGTH ••..••.•••••••....•.••••.•..•...............•.........•.....•....••.......•••••.••••...•..•.••• 813.4 CORROSION EFFECTS ON SHIP STRUCTURES PUBLISHED RESEARCH .••••.••••••.••••••..•••.•••.··•·••••••••••••••••.843.4.1 INTRODUCTION •••••••...••.••••.••••••.•••••••••••••••••....••••••••.•••••••..••.•.•...•.•••..••..•••.•.•••...•••••••..•..•...•.•.•.••••••.••. 843.4.2 CORROSION MODELLING .•••..••.•••••.•••....•••••••••••.••••.••••.•••••.•.••••.•••..•.••••.•..•.•..•.•••••.•.•..•.•...•••...........••. 853.5 STILL WATER LoADS CRITICAL REVIEW OF WORK ...•.••••••••.••...••.••........•....••....•.•.•..••..•..................•. 863.6 WAVE-INDUCED LOADS •••..•••.••••..••.••••..•••..•.•...•.•...•....••...•.••..••.•..••..•....•........•...••......•.•••....•.........•. 86

3.7 LoADCOMBINATION ..•...••..•..•••......•..•.•..•....•.........•.••....•..............••...•....•........•...................•.....••..... 883.8 RELIABILITY BASED STRUCTURAL ANALYSIS •.•••.•..•...••...•................•..•...•...•..•.•...••.•.••.•••...••...•.••••. 893.8.1 INTRODUCTION ••.•••••.••••...•••••.•••.•••..••••••.....•••..•..••••..•....••••.•.•••••.•.•••.••••.••..•••••••.•••..••••...•.••.•.•..•••.••••• 893.8.2 RELIABILITY ANALYSIS ••••..••••••..••••.••...••••..•.......•.••...•..•••••.....••••.••...••.•..•...•••..•.•.•.••.•.••.•...•••....••...•. 893.9 COMBINATORIAL PUBLISHED WORK .....•...••.....••••......•••...........••.•.....•.•....•.•••••••••••••.••.••••...••••...••.••• 913.10 DISCUSSION-REMARKS .........................................•..•..........••...•...............................••..............••.•.••. 93CHAPTER 3, REFERENCES: 95ApPENDIX 3, FIGURES •••.•..••.••......•...•.•..•••.•.•.•.••...•••.•••.•....•••....•.••••••....••..•••.•...•..•.......•....•...••.•...•.....••.•..•.••. 105ApPENDIX 2, TABLES •••••••••••.•.•••••.••.••••.••••.....•••...•••.••••••...••.••....•••.•••••••.••••.••..•....•....•.......••...••..••.•••••.•••••.•.• 108

CHAPTER4

VESSELS & AREA DESCRIPTION & CONSIDERATIONS ..•.••..•••..••.••••.•••••...•.•••....••....••...••••.•.••.•..••.•115

4.1 INTRODUCTION 1154.2 THE FPSO DESIGN CONCEPT HISTORY .•........••••••.•.•.••••••••..•••.••.•.••••.••••.•.••••.•.••••••...••.....••••..•.••....• 1164.3 FPSO IMPLEMENTATION OF DESIGN AND CLASSIFICATION REGULATIONS •...••.....••••...•.•....•.•.••...• 1174.4 FPSO ARRANGEMENTS .•.••••.••...••••••••.••.••.•...•••••.•.•••••••..•••••••••..••..•••••••••....•..•.•.••••.•••••.•••....•••...•••..• 1204.5 FPSO STORAGE AND OFFLOADING .•.•••.•..•••...•.••••••.••....•..•...•...•..••.........•.••••.•...............•...•.•....•.•..• 1204.6 THENoRTHSEA 1214.6.1 GEOGRAPHICAL TERRITORY OF THE WEST OF SHETLAND 1214.6.2 ENVIRONMENTAL ApPREHENSION 1224.6.3 MET-OCEAN CONDITIONS 1234.7 TYPICAL FIELD HISTORY - SCHIEHALLION FIELD 1234.8 DESCRIPTION OF VESSELS ANALYSED 1244.9 DISCUSSION-REMARKS 127CHAPTER 4, REFERENCES: 129ApPENDIX 4, FIGURES 130ApPENDIX 4, TABLES 138

CHAPTERS

THERMAL STRESS ON SHIP STRUCTURES 141

5.1 INTRODUCTION 1415.2 TERMINOLOGY 1415.3 TEMPERATURE CONDITIONS IN SHIP STRUCTURES AND THEIR EFFECTS •...•....•..•••.••..••....•.•••••..•••...• 1425.4 TEMPERATURES PREVAILING AT TIMES OFCASUALTIES 1425.4.1 DEFLECTION 1425.4.2 CHANGE IN THE PROPERTIES OFTHEMATERIAL .•.••••...••••......•..•.....•.•..•••...••••••••..••••...••.....•.••••.•...• 1435.5 TEMPERATURE STRESSES .••...•.••..••.....••••••...•.•...•.•••.••...••...•...••.••...••••.•.••.....•.•...•••••.•...••.....•••..•••..•• 1435.6 FLUCTUATIONS INMARINE STRUCTURAL TEMPERATURES 1475.7 TEMPERATURE DIFFERENTIALS 1495.8 CALCULATION OF TEMPERATURE GRADIENTS •.•.••••••..•••.•••....•.•••....•.•..••••.••••••••..•..••....••....•••..••.•••. 1525.9 CALCULATION OF TEMPERATURE STRESSES ..•••••.••.•••••••••••..•.•....•...•••..•.••...••..••.....••.•.••....•••...•.•.•.. 1535.9.1 ELEMENTARY THERMAL STRESS RELATIONSHIPS 1535.9.2 THERMAL STRESSES ON ABox GIRDER 1555.10 EXPERIMENTAL DATA ON TEMPERATURE STRESSES & Puu, SCALE MEASUREMENTS .•...•.....••..•.. 1625.11 METOCEAN CONDITIONS & TEMPERATURE STATISTICS NORTH SEA .•..••••••••.•••••••.••••..•..••...••...••••• 1655.12 TIME-DEPENDENCY INTEMPERATURE EFFECTS 1665.13 DISCUSSION-RESULTS 1675.13.1 RESULTS OBTAINED 1675.13.2 PROPOSAL ON EXPERIMENTAL PROCEDURES 1695.13.3 METHODS OF ALLEVIATING TEMPERATURE EFFECTS ON SHIPS 172CHAPTER 5, REFERENCES: 175ApPENDIX 5, FIGURES 177ApPENDIX 5, TABLES 193ApPENDIX 5, ADDITIONAL THEORY 197

CHAPTER6

ULTIl\fA TE STRENGTH OF SHIP STRUCTURES 199

6. 1 INTRODUCTION•••..•••••••••.•••••......•...••••••••....•..•••.•..•..••..•••.••••••••••••.••.•.••••••••.••••.•••••••••••••••.••••..•.•.•••••1996.2 UNCERTAINTIESIN THECALCULATIONOFUS .•••.•••.••.•..•..•••.•••.••.•.•••..•.•.••••..•••••••••••.••...••..•..••.•.•..••2026.3 BEHAVIOUROFUNSTIFFENEDPLATES•••••••••••••.•.•.•••..••••..•••..•••••••••...••.•.•••••••..••••••••••••..•••.••.••..••••••2046.3.1 PARAMETERSINFLUENCINGSTRENGTH.••••••.•••.••••••••....••.•••.•.••••••••••..••••.••••.••••..••••.•••••••.•••••...•••••••.2046.4 BEHAVIOUROFSTIFFENEDPLATES••••••.•..••••••••••••••.••••••••••••••••.••.•.•••.••••.••.•..••••.••.••••••.•.••••••.•.•••••••.2056.4.1 PARAMETERSINFLUENCINGSTRENGTH.••.••••••••••..•.•••.•.•..•..•.•••••..•.......•.•..•..•.•.••••.•.•••.••.••..••.••..••.•••2056.5 ULTIMATE STRENGTHOFUNSTIFFENEDANDSTIFFENEDPANELSEXISTINGLITERATURE..•...•..•.•••2076.6 ULTIMATE STRENGTHOFHULL GIRDERSEXISTINGLITERATURE.•.••••.•.••••••••••••••••...•••••••••..•.••.••••.2076.7 MODELLINGTHEULTIMATE STRENGTHOFHULL GIRDERS...•••.•.••.•••.•••..••.•••....•.•••.••••.•.••...•..•••..•.2086.7.1 GUEDESSOARES(1988) UNSTIFFENEDPANELSANALYTICALMETHOD .•.•...•.•.•...•...•••.••..•...••.•••..•2086.7.2 FAULKNER(1975) STIFFENEDPANELSANALYTICALMETHOD ..•...••......•.••....•••.••..•.•••...••.••.•••...••••2116.7.3 PAIK ANDTHAYAMBALLI (1997) EMPIRICALFORMULATION 2136.7.4 HULL GIRDERULTIMATE STRENGTHMODELS••.•••.••...•..•.•••.•.••..•••...•.•••..••..••...•••••..•••••••..••..•.•••••••2156.7.5 PAIK ANDMANSOUR(2001) ANALYTICAL ApPROACH••.•.....•••••••••...••••..•••••.••••••.••..••....•..•••..•...••••2156.7.6. MODIFIEDSMITHANALYTICAL ApPROACH..•••••.•••....••......•..••....•••....•••...•....•••....••..•••••••.••.•..••••••.•220CHAPTER6, REFERENCE:••••.••••.••••••••••....•..•.••••••.•...••..•.•.•.••..•...••••..•••..•.•...•••......•••••.••.••••......•.•••.••••••••.•.•••••231ApPENDIX6, FIGURES•.....•••.•••••••••••••.••...••...•.••••....•••..•••••.••.••....•.•..•....••••••••••....•..•••.•...•••••••••••••••••••••••..•••.••235ApPENDIX6, TABLES ••.•.•..••••••••••...••••...•..•.•.•..•••••.•••.••...••.••.••••..•••.••.•.•..•.....••.•.•....•...••...••••••.....••..••••.••..•••••247

CHAPTER7

CORROSION EFFECTS ON SHIP STRUCTURES •••••..••.••.••.•..•••••••••.••••••.•••••..•.•••••...••••...••••••••••••••..•••••249

7.1 INTRODUCTION••.•••.••..••...•..••••.•.•••••••.••.•..••••.••••..•••••.••••••••••••.•••.•.••••..•••.•••..••••••••••••.•••....•••••.•••......2497.2 CORROSIONMECHANISM.•••••••..••••.••..••••....•.•..••••.•••••.•.••••.•.•..••••••••••••.••••••.....•••••••••.••••.••••••••.••••••••2507.3 GENERALFORMSOFCORROSION.•••...••••..•.•.••.•••.•.•.••••.••.•••••.•.••.•••.••...••.••••...••.••••••••••••..••.••••.••••••..2527.4 CORROSIONIN THEMARINE ENVIRONMENT••..••...•••••••••.•••••..•.•.•••.••.••.••••••.•.•••..••..•.•••..•••.••••.••••••..2557.5 MECHANICSOFCORROSIONINTANKERlFPSO STRUCTURES.....•.......•.••••••••.•••.•..••.•••..•••.•••..•.......2557.6 CORROSIONMODELS•...•....•.......................•...••.•.•.............•••.•....•....•........••....•..••......•....•••.•.•..•...••. 2607.6.1 LINEAR CORROSIONMODEL [PAIK, LEE, HWANGANDPARK (2003)] ••••.••.••.•..••.••....••....••..•.•.••••.•2627.6.2 NON-LINEAR CORROSIONMODEL [GUEDES-SOARES& GARBATOV(1999)] ...•••••....•••..••••......•••.•2647.6.3 COMBININGCORROSIONMODEL [QIN ANDCUI (2001)] .•...•..••••••••••.•.•.••..•.•••.•.••••••••.....•..••..••.••••.•2667.7 OTHERTYPESOFCORROSION.•••.••••....•...••...••.•.........••..........••.•..•••...•.••••.•.....••.•......•••..•.•..••••.•......2687.8 DISCUSSION-CONCLUSIONS•••.•••..•••••..••..••••..••....••••...•.••.••••..••......•••...•...•••...••..••.•.•.••••...•..•••.••...••.2707.8.1 RESULTS.•••••.••.•••.•...•••..••...•.••..••..•••••..••.•••••..•••••••......••...•••.•......••...••....••..•••.....••..•....••.......••..•••.••.2707.8.2 PROPOSALONALTERNATIVECORROSIONFORMULAnON 272CHAPTER7, REFERENCE:...••••••.••••••••..••..••••••••••••..••••••••••••••••••••••.•...•.••.....•••••••••......••••.••.•.•••...•....••••••..••.•••.274ApPENDIX7, FIGURES 276ApPENDIX7, TABLES •.••••••.••••••.••••.•••••.•••••••.•.•.••••....•.•...••••••.••...••••••••••••••.••....•••••.•.••••••....•.••.•....••.••..••••...•.•284

CHAPTERS

LOADS, STOCHASTIC PROCESSES AND THEIR COMBINA TION .••..••••••••.•.••••..........•..•..••.••.•.••••.•286

8.1 INTRODUCTION.•..•••....•.•..•.•.•••••••.•••••.••....•.•...•.•••••••...•.•...•.•.•••••••••..•••••.•....••....••••••••..•••.•••••.••.••.••..2868.2 MET-OCEAN CONDITIONSNORTHSEA ......•.•.•••..••.....•••.••..•.............••.•.......••....••••....•••.•.•.•.••.••..••.•2898.3 ASSUMPTIONSMADE.•..••..•••••••••••••.•...••..•.•••.....•...••.•.••.•..•.••...•••..••....•••......••••....••.•...••..•..••••..•••••..•2908.4 MODELLINGSTILLWATER BENDINGMOMENT (SWBM) .••.•.••...••...•••.•••.•.•......••....••..•.•.••.•••••.•••••2918.5 MODELLINGVERTICALWAVE BENDINGMOMENT (VWBM) ••.•••....•.•.•..••.••....•••...•.•••.•.••..••...••••..2958.6 METHODSOFLOAD COMBINATION.....•••.•.•..••••••••••...•....••••••...•••.••••..•.••••••.••••..•.••••.••••..••.••..••..•.••..2988.6.1 GENERALFORMULATION•.••••..•••.••......•••.••...•.•..••..••.•.••..••••••.....••...•....•••.......•....••••..•••..••••••••••••••.•.2998.6.2 POINTCROSSINGMETHOD.•...•••••.•••........••...•••..•••.••..••.....•.••......•••••.•..••••••••..••..•••••..•••..••..•..•.••...•..3028.6.3 LOAD COINCIDENCEMETHOD••••..••.••..•••.•••..•.•.••••.•...••••.••••••..•.••..•••....•••••••••••.•.••••.•.•••..•••.•..•.•.••.•••3038.6.4 FERRYBORGESAPPROACH.••.••••..•••••..•••.••••.•••..•.•.••..•••.••••.••..•.•••...•••...•.•••••...•..•..••••..•••.••.•••••••••••••3038.6.5 PEAKCOINCIDENCEAPPROACH..••..•..••••...••.••••••.•••...•..•..•.••.•••••.•••...•••••.•.••••••••...•.••••.•...•••.•.••••••.•••3048.6.6 TURKSTRA'SRULEApPROACH 3048.6.7 SRSS RULEApPROACH 3058.7 MODELLINGSLAMMING 3068.8 lACS LOADING 3138.9 APPROACH 314

8.9.1 INTRODUCTION .••••...•••...••••••....••••.••••...••••..•••••••....••..•••••••.••.••...•••..••...•••••..•..•....•.••.•..••...•.••...••...••• 3148.9.2 FERRY BORGES-CAST ANHETA METHOD .•••••••...•......•..•........•..••...•..•...•...••••..•.••....••..•......••...••......• 3178.10 DISCUSSION-CONCLUSIONS •.••...••...•••••••••.•••••••....•••.•••..••.•.•.•....•...•....•.•....•...•....•...•..••...••.••..•..•.•.•. 3198.10.1 COMPARING THE LOAD COMBINATION METHODS .....•......••••.•...•...•••.••.....•.•....•....•....•...•...••...•• 3198.10.2 CALCULATED LoADING •••••..••..•••..•••••••••..••..••.••..•.•••••••••••.•...•.••.•...••..••••••.•••..•••••.••.••••.••.••••..•.•• 320CHAPTER 8, REFERENCES: .•..•••..•••...••••••.•.••...•.•••••••••.••.••..•••••...•.•••.•..••••••..••••••...••....•.•••••..•••...•••..•••..•..•••.•.•• 326ApPENDIX 8, FIGURES •••••••••••.•.•.••••..•.•.•••.••.••.•••••••••••••••.•••...•••..••••••••...•••...•••.•••....•..•.•••••....•••.•.••...•.•..•••.....• 329ApPENDIX 8, TABLES ••..•.•••.•..••••..••.••••••.•••..•••..•.•.•••.•...•.•••.....•....•..•••••..•.•...••••.•••....••.•••.••.•.....••••.••..•..•••..•••. 340

CHAPTER9

RELIABILITY 343

9.1 INTRODUCTION .•••..•••••••••..•••••...••.•.••••.••.•••••..••••••.••..••..••....•••••....••.••••.•••••.•....•••••.•••••.•.....•••.•..•.•.•• :3439.5 FORM & SORM RELIABILITY METHODS •••••......•••.•••.•••••.••..•.....••...••••..•••••.......•..•...••..••..•.•••••..••• 3519.5.1 INTRODUCTION •..•...••...••••..••.••••..•.•.••..••...•..•.••.•..•••••.•••..•••.•...•.••...•••..•••.••.•••.••.•...••••.••••.•.•..••.•.•••... 3519.5.2 FORM ..•••••.•••.•.••..•••••...•••..••.•.•••...•••.••••.•.••••..••••.....•...•....•••.....•••.••.••••.••.•..••..••••.•••.••...•.•.••••.•....•••. 3549.5.3 SORM •••••••.••.•..••..•••..................•............•••••....•••••...•..•.......••..•...•••..........•...••....•..••.........•.••.••...•.•• 3569.8 MONTE CARLO SIMULATION •••••••••....•••••.••.•.•••.••..•••.•••••..•..•••..•..••...•.•....•.•..••.••.•••.•..•.••...•••.••.••••..• 3679.8.1 INTRODUCTION ••....•••••.••••....••.••.••.•••...••••.••••..•••..••.•••..•.•.••..•.••••..•.•...•.••.•..•••.••.•.••••••...•.....•••••.•..•.•• 3679.8.2 RANDOM VARIATE GENERATION •••.•••.••...•.••.•.•••••••••••.•.••.••••..•.••...•.•....••.•..•••.•....••.•••••••.••••••••••....•. 3699.8.3 DIRECT SAMPLING - CRUDE MONTE CARLO .•••.•.••••...•..•......•....•.•......•.........••....•••••....•••......••....•..• 3709.8.4 NUMBER OF SAMPLES REQUIRED .•••.••.•.••••••..•••.•....••.•••••••••••.••••..•••....•••..•.••.•.•••..••.••..•.••...••••••...•••• 3719.9 THE LIMIT STATE EQUATION & STOCHASTIC MODEL •....••.•..••••.•••••.••••••••.••..•••.....•..•.••.•.••....••..•.•. 3729.10 TIME INVARIANT RELIABILITY RESULTS •••••.••..•••••..••..••.•••.••.•..•.....••.•..•••.••••••...••..•..•.•..•••.•.••....•..• 3779.11 TIME VARIANT RELIABILITY RESULTS •••...••.•••.•..•••...•.....•..........••...••....•••.......•.••..•.•..••...•...••...••... 3789.11 DISCUSSION-CONCLUSIONS •...••.....•......••.•.......•.•.•.•.............•.•••................•..••....•••••..••••••.•....•...•.••. 379CHAPTER 10,REFERENCE: ..•.•.•..•••.•..•...••....••••....•..•••..••••••••.•••.•••.•••••....••.•••••••.••••..••....•••..•••••.•.•••..•....••..••••• 384ApPENDIX 9, FIGURES ., .•..••.••.••••...•••••.•..•••..•••••..••..••••.••••.••••..•..•.•..••••...••.•.••••..•••.•...•••••••....••••..•••..••..•••..••... 388ApPENDIX 9, TABLES •.••••.••...•.•••.•...•••••..•••..•..••.••••.•••••••••••••••..•••••.•••••••.••••••••...•.•...•••••••••..••••••••••••••••••••...••..397

CHAPTERIO

DISCUSSION & CONCLUSION •••••••••••••••••••••.••••••••••••••••••••••••••••••••••••••••••••••••••••••••••.••••••••••••••••••••••••••••••••400

10.1 INTRODUCTION 40010.2 THERMAL STRESSES ON MARINE STRUCTURES .40010.3 ULTIMATE STRENGTH 40410.4 CORROSION MODELING 40910.5 LOAD EFFECTS MODELLING 41010.6 TIME INVARIANT AND TIME VARIANT RELIABILITY ANALYSIS .41410.7 FuTuRE RESEARCH 41610.8 CLOSURE 420

THESIS LAYOUT

This thesis adheres to the Guidelines for Presentation of Theses as set by the Glasgow

University Library and the British Standard BS4821: 1990, British Standard

recommendations for the Presentation of theses and dissertations.

The thesis is arranged into 10 chapters each of which has its own tables, figures and

references placed at the end of each chapter. The references are organised alphabetically and

can also be found at the end of the thesis. The numbering system for equations, tables and

figures and references starts with the chapter number in front followed by the number of the

equation. References to figures or equations are placed within parentheses whereas citations

and bibliographical references follow the Harvard system with references by the author's

name and date in the text and the list at the end of each chapter in alphabetical order.

The word processing application used to prepare all chapters of this thesis has been MS

Word 2003 for Windows throughout the entire length of the text. However several other

software packages have been used for the analysis of data, calculations and in the

preparation of this thesis, namely: MS Visual Studio for Fortran compiling, MS Excel 2003

for Windows and Visual Basic, Mathsoft MathCAD 13.0, Lloyd's Register LRPASS, DNV

PROBAN, DNV WASIM, RCP Consulting COMREL and various other graphing and

reporting tools.

SUMMARY

In the beginning of this thesis, in Chapter 1, an introduction is given on the concepts of

rationally based structural design and how this has developed to extend today to reliability

based code formats, some of which are explained in detail with particular emphasis on the

definition of limit states, modelling of environmental characteristics and how the different

load components are combined. The trend to limit state based code formats is recognized

and the need to develop a framework that takes into account as much detail of

environmental loading as possible is identified.

In Chapter 2 the problem of global warming & climate change is discussed and it is made

evident from the relevant literature that very limited analysis and data exist on this particular

problem. Thermal effects on marine structures are ignored in most of the cases studied or

appear to have been somehow neglected. Emphasis is placed on casualties resulting from

such phenomena and under what conditions such failure might occur. Particular emphasis is

also placed in the extreme nature of loadings that affect marine structures, especially with

modem climate changes that appear more evident in the last 10 years.

Chapter 3 reviews in a critical manner all literature that was available during this study.

Each individual element of this study is examined providing information on the significant

research over the last 50 years, with particular emphasis on the thermal effects on marine

structures, various types of loading imposed on the structure and the ultimate bending

moment modelling of marine structures that would enable reliability analysis to be

performed for a particular type of structure. The issues of corrosion and slamming effects on

marine structures are also critically reviewed as they are identified of particular importance

to marine structure and the environments under which they operate. Suggestions on the

possible approaches that this research might follow are made in the concluding sections of

this chapter.

In Chapter 4 the type of vessel to be analysed is described in detail along with the history of

its development and operational procedures that formulate its unique characteristics. The

vessels to be analysed are described in detail and a thorough description of the area they

operate and its unique geographical and climatological conditions is made. This provides a

thorough understanding of the nature of the problem to be investigated and will enable a

detailed study to be carried out based on the actual conditions that prevail in the particular

area.

Chapter 5 contains detailed evaluation of some of the procedures that already have been

adopted for thermal analysis of ship structures in an attempt to define their limitations and

scope their applicability. A detailed procedure for analysing the structures and the effects of

diurnal temperature changes is described based on thermal stress theory and analysis of

statistical data obtained from the actual area of operations of the vessels analysed,

demonstrating the significant effect that it may have on the safety of the structure under

extreme conditions. All theoretical background behind the approaches is described in detail

and commented upon. Analysis is carried out for the vessels in question using the proposed

procedure and some of the results obtained are discussed briefly.

Chapter 6 describes an investigation of the best possible way of modelling the ultimate

strength of the hull girder for the vessel analysed. A variety of different approaches, each

described in detail throughout the chapter, are developed into a code entitled MUSACT that

uses a variety of formulation and approaches, both empirical and semi-analytical to

investigate the effect of the formulation on the results. The ultimate strength of stiffened and

unstiffened plates is formulated in the code and combined using closed form and

progressive collapse analysis formulation. All theoretical background behind the approaches

is described in detail and commented upon. From the results obtained it is evident that the

overall hull girder strength can significantly vary depending on the combination of

approaches used. The results obtained also investigate the effect of various corrosion

formulations on the ultimate strength as described in Chapter 7. Results obtained for the as

built condition of the vessels are validated against commercial codes used by a major

Classification Society and experimental data available in the published literature.

Chapter 7 describes the nature of the corrosion phenomenon in marine structures and the

various forms it can take, both physically and chemically. Various approaches proposed for

modelling the corrosion wastage on various parts of marine structures are discussed, both

linear and non-linear and are incorporated into the MUSACT code for the determination of

the overall hull girder ultimate bending moment. The combined ultimate bending moment

and corrosion results are presented forming the basis for the resistance part of the limit state

equation to be used for reliability analysis. All theoretical background behind the

approaches is described in detail and commented upon.

In Chapter 8 the load imposed on the structures analysed and their nature is discussed and

particular emphasis is placed in the vertical bending moments acting on the structures. Still

water loads and vertical wave bending loads and their extreme responses are discussed and

the stochastic natures of the phenomena are described in detail. Both short term and long

term formulation for the description of the loads experienced is used to formulate the

loading components required for reliability analysis. All theoretical background behind the

approaches is described in detail and commented upon. The effect of impulsive loads like

slamming and green water on deck on the wave-induced bending moment is estimated by a

semi-analytical approach. The impulse loads leading to transient vibrations are described on

terms of magnitude, phase lag relative to the wave-induced peak and decay rate. The

stochastic nature of all loading components is also investigated and the best possible way

for combining the extreme responses is investigated.

Chapter 9 describes the structural reliability analysis performed and the results obtained

both from time-invariant and time-variant analyses using second moment and simulation

methods. Uncertainties in the analysis and their nature are described and the best way for

combining all the elements investigated throughout the study is investigated. A stochastic

model and limit state function for time-variant and time-invariant analysis is proposed

forming failure criterion used by the reliability methods used. All theoretical background

behind the approaches is described in detail and commented upon. The effect of thermal

stresses and corrosion in the probability of failure and the reliability indices obtained is

demonstrated.

Although results are presented in each individual chapter, Chapter 10 provides a wider,

overall discussion on the results obtained, their significance and comments upon the theory

used throughout this thesis. Proposals are made on future research and experimentation that

will complement the study carried out but also methods to reduce phenomena such as

excessive thermal stresses and corrosion.

LIST OF FIGURES BY CHAPTER

CHAPTER 1FIGURE 1.1 (LEFT) HIGHEST AND LOWEST AIR TEMPERATURE WITH AN ANNUAL

PROBABILITY OF EXCEEDANCE OF 10-2 • (MIDDLE) HIGHEST SURFACE TEMPERATURE INTHE SEA WITH AN ANNUAL PROBABILITY OF EXCEEDANCE OF 10.2• (RIGHT) LOWESTSURFACE TEMPERATURE IN THE SEA WITH AN ANNUAL PROBABILITY OF EXCEEDANCEOF 10.2• THE TEMPERATURES ARE GIVEN IN DEGREES CELSIUS. (NORSOK N003, 1999) 52

FIGURE 1.2.CURVE BENDING MOMENT CAPACITY M VERSUS CURVATURE X (BV, 2004) 52FIGUREl. 3. FLOW CHART OF THE PROCEDURE FOR THE EVALUATION OF THE CURVE M-X

(BV, 2004) 53

CHAPTER2FIGURE 2.1 COMBINED ANNUAL LAND, AIR AND SEA SURFACE TEMPERATURES (1860-2002)

RELATIVE TO 1961-1990. (WMO 2(02) 70FIGURE 2.2 GLOBAL SIGNIFICANT CLIMATE ANOMALIES IN 2002 (WMO 2(02) 70FIGURE 2.3 PRECIS OUTPUT (HADLEY CENTRE 2005) 71FIGURE 2.4 PRELIMINARY MAP OF BASE WIND SPEEDS FOR THE UK (THE STRUCTURAL

ENGINEER 2(03) 71FIGURE 2.5 TREND IN DECENNIAL EXTREME WINDS 1970-1999 FOR THE UK (THE

STRUCTURAL ENGINEER 2(03) 72FIGURE 2.6 CORROSION IN BALLAST TANKS (HUGHES 2(05) 72FIGURE 2.7 AIR TEMPERATURE AND TEMPERATURE GRADIENT AT TIME OF FRACTURE.

(HECHTMAN 1956) 72

CHAPTER3FIGURE 3.1 MEAN AND DYNAMIC HULL STRESSES ON A CONTAINER SHIP (SHI ET AL, 1996) .

................................................................................................................................................................ 105FIGURE 3.2 TEMPERATURE GRADIENT BETWEEN THE INNER AND OUTER WALLS ON A

CONTAINER SHIP (SHI ET AL, 1996) 105FIGURE 3.3 TEMPERATURE READINGS OVER SEVERAL DAYS AT THE LONGITUDINAL

BULKHEAD AND SIDE SHELL (SHI ET AL., 1996) 105FIGURE 3.4 PORT TEMPERATURES AND MEAN HULL STRESSES (SHI ET AL., 1996) 106FIGURE 3.5 MEAN HULL STRESSES DURING ONE DAY TEMPERATURE CYCLE (SHI ET AL,

1996) 106FIGURE 3.6 HULL THERMAL STRESSES UNDER SYMMETRICAL (LEFT) AND ASYMMETRICAL

(RIGHT) TEMPERATURE GRADIENTS (SHI ET AL., 1996) 106FIGURE 3.7 DISTRIBUTION OF SWBM OF CONTAINER SHIPS (MANO, 1977) 107

CHAPTER4FIGURE 4.1 THE 'GLAS DOWR' FPSO. (MARIN, 2(05) 130FIGURE 4.2 THE 'TRITON' FPSO (HESS, 2(05) 130FIGURE 4.3 THE 'SCHIEHALLION' FPSO (SHELL, 2(05) 130FIGURE 4.4 'ANASURIA' FPSO (MITSUBISHI HEAVY INDUSTRIES LTD, 2005) 131FIGURE4.5 GROWTH IN THE WORLD'S FPSO FLEET 1985-2001, (BLUEWATER 2(05) 131FIGURE 4.6 DISTRIBUTION OF THE WORLD'S FPSO FLEET, (BLUEWATER 2005) 132FIGURE 4.7 FPSO OWNERSHIP, (BLUEWATER 2(05) 132FIGURE 4.8 TERRA NOVA FPSO DECK AND OPERATIONAL ARRANGEMENTS, (TERRA NOVA

PROJECT, 2005) 133FIGURE 4.9 TERRA NOV A FPSO OFFLOADING OPERATIONAL ARRANGEMENTS, (TERRA NOV A

PROJECT, 2(05) 133FIGURE 4.10 THE WEST OF SHETLAND AREA OF SCOTLAND 134FIGURE 4.11 ENVIRONMENTAL CHARACTERISTICS COMPARISON OF THE WEST OF SHETLAND

AND THE NORTH SEA 135FIGURE 4.12 THE FOINA VEN, SCHIEHALLION AND LOYAL FIELDS 135FIGURE 4.13 ANASURIA FPSO STRUCTURAL DETAILS & CONFIGURATION 136FIGURE4.14 SCHIEHALLION FPSO STRUCTURAL DETAILS & CONFIGURATION 136FIGURE 4.15 TRITON FPSO STRUCTURAL DETAILS & CONFIGURATION 137FIGURE 4.16 FUTURE FPSO INSTALLATIONS, (DOUGLAS-WESTWOOD, 2003) 137

CHAPTER5FIGURE 5.1 COMPUTED THERMAL STRESS IN SHELL & DECK PLATING OF T2 TANKER FOR

DIFFERENT DRAFTS WITH LBHD AT 0°, (HECHTMAN, 1956) 177FIGURE 5.2 COMPUTED THERMAL STRESS IN SHELL & DECK PLATING OF T2 TANKER FOR

DIFFERENT DRAFTS WITH LBHD AT lo°, (HECHTMAN, 1956) 177FIGURE 5.3 COMPUTED THERMAL STRESSES IN T2 TANKER WITH SUN AT PORT SIDE,

(HECHTMAN, 1956) 178FIGURE 5.4 TEMPERATURES AND RADIATION CONTROL PLOT, (HECHTMAN, 1956) 178FIGURE 5.5 TEMPERATURE CHANGES ON TRANSVERSE AND LONGITUDINAL TEST SECTION

(CORLET, 1950) 179FIGURE 5.6 TEMPERATURE CHANGE IN TRANSVERSE SECTION FOR 10°F DIFFERENCE

BETWEEN AIR &WATER TEMPERATURE (HECHTMAN, 1956) 180FIGURE 5.7 EFFECT OF COLOUR UPON TEMPERATURE OF HORIZONTAL SURFACES

SUBJECTED TO INSOLATION. (HECHTMAN, 1956) 180FIGURE 5.8 TEMPERATURE GRADIENT RESULTING FROM DIFFERENCE IN COLOUR SURFACE

(MERIAM ET AL., 1958) 181FIGURE 5.9 SCHEMATIC DIAGRAM OF THREE-DIMENSIONAL TEMPERATURE VARIA TION IN

STRUCTURAL CORNER 181FIGURE 5.10 ELEMENTARY THERMAL STRESS MATERIAL DEFINITIONS 182FIGURE 5.11 TEMPERATURE GRADIENTS IN BEAM WITH RECTANGULAR CROSS SECTION 182FIGURE 5.12 IDEALIZED GIRDER OF UNIFORM CROSS SECTION THROUGHOUT ITS LENGTH

WITH CONNECTIONS BETWEEN THE SIDES OF THE BOX ASSUMED HINGED 183FIGURE 5.13 NON APPLICABILITY OF THERMAL STRESS DISTRIBUTION THEORETICAL

SOLUTION NEAR THE ENDS OF BEAM 183FIGURE 5.14 ASSUMED SYMMETRICAL TEMPERATURE DISTRIBUTION, (JASPER, 1956) 184FIGURE 5.15 ASSUMED ASYMMETRICAL TEMPERATURE DISTRIBUTIONS" (JASPER, 1956) 184FIGURE 5.16 TEMPERATURES AND CORRESPONDING THERMAL STRESSES ON TRANSVERSE

AND LONGITUDINAL TEST SECTIONS (MERIAM ET AL., 1958) 185FIGURE 5.17 TEMPERATURES AND CORRESPONDING THERMAL STRESSES ON TRANSVERSE

AND LONGITUDINAL TEST SECTIONS, MERIAM ET AL. (1958) 185FIGURE 5.18 FAIR ISLE WEATHER STATION LOCATION 186FIGURE 5.19 MONTHLY AVERAGE DIURNAL CHANGE IN T (FAIR ISLE) 1978-1998 186FIGURE 5.20 MONTHLY HIGH, LOW AND AVERAGE AIR TEMPERATURE (FAIR ISLE) 1989 187FIGURE 5.21 MONTHLY AVERAGE CLOUD COVER (FAIR ISLE) FOR YEARS OF AVERAGE

EXTREME T CHANGES 187FIGURE 5.22 AVERAGE SEASONAL DIURNAL THERMAL STRESSES ON TRITON FPSO

STRUCTURAL ELEMENTS 188FIGURE 5.23 EXTREME SUMMER DIURNAL THERMAL STRESSES ON TRITON FPSO

STRUCTURAL ELEMENTS 188FIGURE 5.24 EXTREME WINTER DIURNAL THERMAL STRESSES ON TRITON FPSO

STRUCTURAL ELEMENTS : 189FIGURE 5.25 EXTREME FALL DIURNAL THERMAL STRESSES ON TRITON FPSO STRUCTURAL

ELEMENTS : 189FIGURE 5.26 EXTREME SPRING DIURNAL THERMAL STRESSES ON TRITON FPSO STRUCTURAL

ELEMENTS 190FIGURE 5.27 US VARIATION ON THE OUTER SHELL OF THE STRUCTURE RESULTING FROM

DIURNAL THERMAL STRESSES FOR ALL SCENARIOS (TRITON FPSO) 190FIGURE 5.28 US VARIATION ON THE INNER SHELL OF THE STRUCTURE RESULTING FROM

DIURNAL THERMAL STRESSES FOR ALL SCENARIOS (TRITON FPSO) 191FIGURE 5.29 US VARIATION ON THE CENTERLINE OF THE STRUCTURE RESULTING FROM

DIURNAL THERMAL STRESSES FOR ALL SCENARIOS (TRITON FPSO) 191FIGURE 5.63 STRAIN GAGE BEAM DEFINITION 192FIGURE 5.31 COMBINED STRESS DISTRIBUTION ON BEAM AS A RESULT OF AXIAL FORCE 192FIGURE 5.32 STRAIN GAGE LOCATION ACCORDING TO POLYNOMIAL DISTRIBUTION 192

CHAPTER6FIGURE 6.1 STIFFENED PLATE DEFINITIONS (FAULKNER 1972) 235FIGURE 6.2 EQUIVALENT SECTION CONFIGURATION OF A SHIP'S HULL. 235FIGURE 6.3 LINEAR DISTRIBUTION OF LONGITUDINAL AXIAL STRESSES IN A HULL SECTION

................................................................................................................................................................ 235

FIGURE 6.4 PRESUMED LONGITUDINAL STRESS DISTRIBUTION OVER HULL CROSS SECTIONAT OVERALL COLLAPSE STATE 236

FIGURE 6.5 COMBINED BENDING OF THE HULL GIRDER 236FIGURE 6.6 MUSACT VB CODE FOR MS EXCEL 2003 236FIGURE 6.7 MUSACT VB CODE FOR MS EXCEL 2003 SOURCE CODE 237FIGURE 6.8 EFFECT OF VARIOUS US FORMULATION ON OB STIFFENED PANEL AVERAGE US

(ANASSURIA FPSO) : 237FIGURE 6.9 EFFECT OF VARIOUS US FORMULATION ON SS STIFFENED PANEL AVERAGE US

(ANASSURIA FPSO) 238FIGURE 6.10 EFFECT OF VARIOUS US FORMULATION ON DECK STIFFENED PANEL AVERAGE

US (ANASSURIA FPSO) 238FIGURE 6.11 EFFECTS OF VARIOUS CORROSION AND US FORMULATION ON HOGGING HULL

GIRDER US (ANASSURIA FPSO) 239FIGURE 6.12 EFFECfS OF VARIOUS CORROSION AND US FORMULATION ON HOGGING HULL

GIRDER US (ANASSURIA FPSO) 239FIGURE 6.13 SAMPLE STRESS-STRAIN CURVE OUTPUT FROM LRPASS FOR TRITON FPSO 240FIGURE 6.14 TRITON FPSO SAGGING US USING LRPASS 240FIGURE 6.15 TRITON FPSO HOGGING US USING LRPASS 241FIGURE 6.16 SCHIEHALLION FPSO SAGGING US USING LRPASS 241FIGURE 6.17 SCHIEHALLION FPSO HOGGING US USING LRPASS 242FIGURE 6.18 ANASSURIA FPSO SAGGING US USING LRPASS 242FIGURE 6.19 ANASSURIA FPSO HOGGING US USING LRPASS 243FIGURE 6.20 LRPASS-MUSACT VALIDATION OF US VERTICAL MOMENT RESUL TS 243FIGURE 6.21 LRPASS-MUSACT VALIDATION OF US VERTICAL MOMENT RESULTS, (TRITON

FPSO) 244FIGURE 6.22 LRPASS-MUSACT VALIDATION OF US VERTICAL MOMENT RESULTS,

(SCHIEHALLION FPSO) 244FIGURE 6.23 COMPARATIVE MUSACf RESULTS FOR ALL FPSOS ANALYSED 245FIGURE 6.24A-C MIDHSIP SECTIONS OF DOWLING'S BOX GIRDER MODELS TESTED IN THE

HOGGING CONDITION (MM) 245FIGURE 6.25A, B MIDSHIP SECTIONS OF NISHIHARA'S BOX GIRDER MODELS TESTED IN THE

SAGGING CONDITION (MM) 246FIGURE 6.26 MIDSHIP SECfION OF MANSOUR'S BOX GIRDER MODEL II TESTED IN THE

HOGGING CONDITION (MM) 246FIGURE 6.27 MIDSHIP SECTION OF ONE-THIRD-SCALE FRIGATE HULL MODEL TESTED IN THE

SAGGING CONDITION (MM) 246

CHAPTER 7FIGURE 7.1 FLOW BETWEEN ANODIC AND CATHODIC AREAS (GORDON ENGLAND, 2005) ..... 276FIGURE 7.2 ANODIC AND CATHODIC AREAS RESULTING FROM SURFACE VARIATIONS

(GORDON ENGLAND, 2005) 276FIGURE 7.3 CORROSION PROCESS IN AN AQUEOUS ELECTROLYTE (GORDON ENGLAND, 2005) .

................................................................................................................................................................ 276FIGURE 7.4 CORROSION OF IRON (FE) IN AN AQUEOUS ELECTROLYTE (GEORGIA STATE

UNIVERSITY, 2005) 277FIGURE 7.5 TYPES OF CORROSION WASTAGE: A)GENERAL, (B) LOCALIZED, (C) FATIGUE

CRACKS FROM LOCALISED CORROSION (PAIK, LEE, HWANG & PARK, 2003) 277FIGURE 7.6 VARIOUS ANODE SHAPES (CRAFT, 1981) 277FIGURE 7.7 PAIK, LEE, HWANG AND PARK PROPOSED CORROSION MODEL (PAIK, LEE,

HWANG & PARK, 2003) 278FIGURE 7.8 GUEDES SOARES AND GARBATOV PROPOSED CORROSION MODEL (GUEDES

SOARES & GARBATOV, 1991) 278FIGURE 7.9QIN & CUI SUGGESTED CORROSION MODEL (QIN & CUI, 2001) 278FIGURE 7.10 SELECTOR FOR ORGANIC COATINGS (FONTANA & GREEN, 1967) 279FIGURE 7.11 STRESS CORROSION CRACKING (JASTRZEBSKI, 1976) 279FIGURE 7.12 S-N DIAGRAM FOR CORROSION FATIGUE (CRAFT, 1981) 279FIGURE 7.13 MUSACT VB CODE FOR MS EXCEL 2003 DISPLAYING CORROSION AND RESULTS

WINDOWS 280FIGURE 7.14 INFLUENCE OF CORROSION MODELS ON DECK PLATING WASTAGE 280FIGURE 7.15 INFLUENCE OF CORROSION MODELS ON BOTTOM PLATING WASTAGE 281

FIGURE 7.16 INFLUENCE OF TRANSITION TIME ON THE NON-LINEAR GUEDES SOARES &GARBATOV (1999) MODEL 281

FIGURE 7.17 INFLUENCE OF LONG TERM CORROSION DEPTH IN THE GUEDES SOARES &GARBATOV (1999) NON-LINEAR MODEL. 282

FIGURE 7.18 EFFECTS OF VARIOUS CORROSION AND US FORMULATION ON HOGGING HULLGIRDER US (ANASSURIA FPSO) 282

FIGURE 7.19 EFFECTS OF VARIOUS CORROSION AND US FORMULATION ON HOGGING HULLGIRDER US (ANASSURIA FPSO) 283

CHAPTER 8FIGURE 8.1 TYPICAL EXTREME (lOOYR) WAVE HEIGHTS, (IMAREST, 2004) 329FIGURE 8.2 CENTRAL NORTH SEA WIND SPEEDS (MIS), (IMAREST, 2(04) 329FIGURE 8.3 FPSO WIND TUNNEL TESTING, (THE NAVAL ARCHITECT, 2004) 329FIGURE 8.4 MODELLING OF SWBM BY A POISSON RECTANGULAR PULSE PROCESS 330FIGURE 8.5 SAGGING SWBM DISTRIBUTION IN PRODUCTION SHIP, (MOAND & HAO, 1988) 330FIGURE 8.6 LONG-TERM DISTRIBUTION OF DECK STRESSES RESULTING FROM VWBM,

(FRIEZE ET AL., 1991) 330FIGURE 8.7 REALIZATION OF PROCESS X(T) SHOWING CLUMPING EFFECT AND BARRIER

CROSSING 331FIGURE 8.8 LOAD COINCIDENCE FOR RECTANGULAR PULSE PROCESSES, (WEN 1990) 331FIGURE 8.9 FERRY BORGES PROCESSES 331FIGURE 8.10 PIECE-WISE PRISMATIC BEAM 332FIGURE 8.11 ASSUMED VARIATION OF BENDING MOMENT WITH BLOCK COEFFICIENT

(JENSEN & MANSOUR, 2(02) 332FIGURE 8.12 FPSO TRITON WEIGHT DISTRUBUTION FOR VARIOUS LOADING CONDITIONS 332FIGURE 8.13 TRITON FPSO CROSS-SECTIONAL OFFSETS 333FIGURE 8.14 TRITON FPSO HULL GEOMETRY MODEL IN AUTOHYDRO 333FIGURE 8.15 ASSUMED OPERATIONAL PROFILE FITTED AS A PULSE PROCESS 334FIGURE 8.16 THE EXTREME SWBM PROBABILITY DENSITY FUNCTIONS FOR 3 LOADING

CONDITIONS (TRITON FPSO) 334FIGURE 8.17 THE EXTREME SWBM PROBABILITY DISTRIBUTION FUNCTION FOR 3 LOADING

CONDITIONS (TRITON FPSO) 335FIGURE 8.18 TRANSFER FUNCTIONS FOR TRITON FPSO FOR FULL LOAD CONDITION 335FIGURE 8.19 ALGORITHM FOR THE CALCULATION OF THE LONG-TERM PROBABILITY

DISTRIBUTION OF WAVE INDUCED LOAD EFFECTS 336FIGURE 8.20 LONG-TERM WEIBULL FIT DISTRIBUTION OF THE VERTICAL BENDING MOMENTS

FOR SCHIEHALLION FPSO 337FIGURE 8.21 ANASSURIA FPSO NON-LINEAR LONG-TERM PROBABILITY OF EXCEEDANCE 337FIGURE 8.22 SCHIEHALLION FPSO NON-LINEAR LONG-TERM PROBABILITY OF EXCEEDANCE .

................................................................................................................................................................ 338FIGURE 8.23 TRITON FPSO NON-LINEAR LONG-TERM PROBABILITY OF EXCEEDANCE 338FIGURE 8.24 LOAD DISTRIBUTION FUNCTIONS FOR TRITON FPSO IN FULL LOAD CONDITION .

................................................................................................................................................................ 339FIGURE 8.25 LOAD DISTRIBUTION FUNCTIONS FOR TRITON FPSO IN PARTIAL LOAD

CONDITION 339FIGURE 8.26 LOAD DISTRIBUTION FUNCTIONS FOR TRITON FPSO IN BALLAST LOAD

CONDITION 339

CHAPTER9FIGURE 9.1 TWO RANDOM VARIABLE JOINT DENSITY FUNCTION FRs{ R,S), MARGINAL

DENSITY FUNCTIONS FR AND Fs AND FAILURE DOMAIN D 388FIGURE 9.2 BASIC R-S PROBLEM: FRf)Fs{) REPRESENTATION 388FIGURE 9.3 BASIC R-S PROBLEM: FRf)Fs{) REPRESENTATION 388FIGURE 9.4 HASOFER-LIND RELIABILITY INDEX: LINEAR PERFORMANCE FUNCTION 389FIGURE 9.5 HASOFER-LIND RELIABILITY INDEX: NONLINEAR PERFORMANCE FUNCTION 389FIGURE9.6 RACKWITZ ALGORITHM FOR FINDING PHL' 389FIGURE 9.7 THE ORDERING PROBLEM IN THE HASOFER-LIND RELIABILITY INDEX 390FIGURE 9.8 POLYHEDRAL APPROXIMATION TO THE LIMIT STATE 390FIGURE 9.9 FITTING OF PARABOLOID IN ROTATED STANDARD SPACE (DER KIUREGHIAN ET

AL, 1987) 391

FIGURE 9.10 SCHEMATIC TIME-DEPENDENT RELIABILITY PROBLEM 391FIGURE 9.11 TYPICAL REALIZATION OF RANDOM PROCESS LOAD EFFECT.: 391FIGURE 9.12 REALIZATION OF SAFETY MARGIN PROCESS Z(T) AND TIME TO FAILURE 392FIGURE 9.13 OUT-CROSSING OF VECTOR PROCESS X(T) 392FIGURE 9.14 INVERSE TRANSFORM METHOD FOR GENERATION OF RANDOM VARIATES 392FIGURE 9.15 USE OF FITTED CUMULATIVE DISTRIBUTION FUNCTION TO ESTIMATE PF •••••••• 393FIGURE 9.16 TEMPERATURE AND CORROSION EFFECT ON PFIN SAGGING CONDITION 393FIGURE 9.17 TEMPERATURE AND CORROSION EFFECT ON PIN SAGGING 393FIGURE 9.18 TEMPERATURE AND CORROSION EFFECT ON PFIN HOGGING 394FIGURE 9.19 TEMPERATURE AND CORROSION EFFECT ON PIN HOGGING 394FIGURE 9.20 TEMPERATURE EFFECT ON THE PARTIAL SAFETY FACTORS IN SAGGING 394FIGURE 9.21 TEMPERATURE EFFECT ON THE PARTIAL SAFETY FACTORS IN HOGGING 395FIGURE 9.22 INSTANTANEOUS AND TIME VARIANT PROBABILITY OF FAILURE 395FIGURE 9.23 INSTANTANEOUS AND TIME VARIANT RELIABILITY INDEX 396

LIST OF TABLES BY CHAPTER

CHAPTER 1TABLE 1.1 DESIGN LIMIT STATES CONSIDERED BY STATUTORY AND REGULATORY BODIES

WORLDWIDE. 54TABLE 1.2 SAFETY CLASSES AND RELIABILITY LEVELS (FREDERKING ET AL., 2004). 55TABLE 1.3 LOAD FACTORS AND LOAD COMBINATIONS (FREDERKING ET AL., 2004). 55TABLE 1.4 CHARACTERISTIC ACTIONS AND COMBINATIONS (NORSOK N003, 1999). 55TABLE 1.5 LOAD ACTION COMBINATIONS (NORSOKNOO4, 1998). 56TABLE 1.6 TENTATIVE TARGET RELIABILITY iNDICES P(AND ASSOCIATED TARGET FAILURE

RATES) RELATED TO ONE YEAR REFERENCE PERIOD AND ULTIMATE LIMIT STATES.(JCSS, 1999). 56

TABLE 1.7 TARGET RELIABILITY INDICES (AND ASSOCIATED PROBABILITIES) RELATED TOONE YEAR REFERENCE PERIOD AND IRREVERSIBLE SLS (JCSS, 1999). 56

TABLE 1.8 PARTIAL SAFETY FACTORS (BV, 2004). 56

CHAPTER2No Tables

CHAPTER3TABLE 3.1 REVIEW OF THERMAL STRESS RESEARCH SINCE THE 1900S IN CHRONOLOGICAL

ORDER. 108TABLE 3.2 REVIEW OF UNSTIFFENED PANELS ULTIMATE STRENGTH RESEARCH SINCE THE

1970S IN CHRONOLOGICAL ORDER. 109TABLE 3.3 REVIEW OF STIFFENED PANELS ULTIMATE STRENGTH RESEARCH SINCE THE 1970S

IN CHRONOLOGICAL ORDER. 1 IOTABLE 3.4 REVIEW OF HULL GIRDER ULTIMATE STRENGTH RESEARCH SINCE THE 1960S IN

CHRONOLOGICAL ORDER. 111TABLE 3.5 SIGNIFICANT CORROSION WORK SINCE THE 1980S IN CHRONOLOGICAL ORDER. 112TABLE 3.6 SIGNIFICANT RELIABILITY ANALYSIS WORK PUBLISHED SINCE THE 1950S IN

CHRONOLOGICAL ORDER. 113TABLE 3.7 SIGNIFICANT COMBINATORIAL PUBLISHED WORK IN ALPHABETICAL ORDER. 114

CHAPTER4TABLE 4.1 TABLE OF OIL COMPANY OWNED FPSOS OPERA TINGIPLANNED TO OPERATE IN

THE NORTH SEA, (BLUEWATER, 1999). 138TABLE 4.2 TABLE OF CONTRACTOR OWNED FPSOS OPERA TINGIPLANNED TO OPERATE IN

THE NORTH SEA, (BLUEWATER, 1999). 138TABLE 4.3 CLASSIFICATION ABANDONED EXAMPLES, (STILL, 2004). 139TABLE 4.4 CLASSIFICATION RETAINED EXAMPLES, (STILL 2(04). 139TABLE 4.5 FPSO PRINCIPAL & OPERATIONAL PARTICULARS. 139TABLE 4.6 FPSO MIDHSIP SECTION PROPERTIES-AS BUILT CONDITION. 140

CHAPTER5TABLE 5.1 PROBABLE MAXIMUM AND MINIMUM AIR TEMPERATURES IN THE NORTH SEA 193TABLE 5.2 VARIATIONS IN SEA SURFACE TEMPERATURE 193TABLE 5.3 DECK COLOUR TEMPERATURE DIFFERENCES 193TABLE 5.4 US CALCULATION SAGGING & HOGGING, NO THERMAL EFFECTS. 194TABLE 5.5 US CALCULATION SAGGING & HOGGING, AVERAGE SEASONAL SCENARIO. 194TABLE 5.6 US CALCULATION SAGGING & HOGGING, EXTREME SUMMER SCENARIO. 195TABLE 5.7 US CALCULATION SAGGING & HOGGING, EXTREME WINTER SCENARIO. 195TABLE 5.8 US CALCULATION SAGGING & HOGGING, EXTREME FALL SCENARIO. 196TABLE 5.9 US CALCULATION SAGGING & HOGGING, EXTREME SPRING SCENARIO. 196

CHAPTER6TABLE 6.1 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FOR ANNASSURIA

FPSO. 247

TABLE 6.2 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FORSCHIEHALLION FPSO. 247

TABLE 6.3 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FOR TRITON FPSO.247

TABLE 6.4 FPSO ULTIMATE STRENGTH RESULTS. 247TABLE 6.5 PROPERTIES OF EQUIVALENT CROSS SECTIONS AND COMPARISON OF ULTIMATE

STRENGTH FORMULATIONS WITH TEST MODELS AND NUMERICAL RESULTS. 248

CHAPTER 7TABLE7.l THE GALVANIC SERIES (CRAFT, 1981). 284TABLE 7.2 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FOR ANNASSURIA

FPSO. 284TABLE 7.3 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FOR

SCHIEHALLION FPSO. 285TABLE 7.4 PERCENTILE DIFFERENCES IN US THEORETICAL MODELS USED FOR TRITON FPSO.

285

CHAPTER 8TABLE 8.1 LOAD COMBINATION FACTORS FOR STILL WATER ANDWAVE-INDUCED BENDING

MOMENTS. 340TABLE 8.2 BLOCK COEFFICIENT FACTOR FcB(CB) 340TABLE 8.3 SAGGING LOAD COMBINATION FACTOR COMPARISON USING DIFFERENT MODELS.

340TABLE 8.4 lACS REQUIREMENTS FOR WAVE AND STILL WATER BENDING MOMENTS. 341TABLE 8.5 CHARACTERISTIC AND EXTREME VALUES OF THE SWBM FOR 3 FPSOS ANALYSED.

341TABLE 8.6 ANASSURIA FPSO COMPARATIVE RESULTS FOR BENDING MOMENT INCLUDING

THE EFFECT OF SLAMMING. 341TABLE 8.7 SCHIEHALLION FPSO COMPARATIVE RESULTS FOR BENDING MOMENT INCLUDING

THE EFFECT OF SLAMMING. 341TABLE 8.8 TRITON FPSO COMPARATIVE RESULTS FOR BENDING MOMENT INCLUDING THE

EFFECI' OF SLAMMING. 342TABLE 8.9 VBM VALUES WITH 0.5 LEVEL OF EXCEEDANCE AND EQUIVALENT LOAD

COMBINATION FACTORS FOR FPSOS ANALYSED. 342

CHAPTER 9TABLE 9.1 RELIABILITY LEVELS AND METHODOLOGY. 397TABLE 9.2 RANDOM VARIABLES RELATED TO INHERENT UNCERTAINTIES IN STRENGTH. 397TABLE 9.3 RANDOM VARIABLES RELATED TO MODEL UNCERTAINTIES. 397TABLE 9.4 STOCHASTIC MODEL USED FOR TIME VARIANT AND TIME-INVARIANT

RELIABLITY ANALYSIS. 398TABLE 9.5 FPSO RELIABILITY LEVELS PUBLISHED SINCE 1990. 398TABLE 9.6 TANKER RELIABILITY LEVELS PUBLISHED SINCE 1990 399

GFUS

American Bureau of Shipping

Advanced First Order Second Moment Method

American Petroleum Institute

1 Barrel = 159 litres = 0.159 m3

Barrels per Day = 50 tonnes per year

Bureau Veritas

Centre of Gravity

Central North Sea

Coefficient of Variation

Corrosion Protection System

Design and Construction Regulations

Det Norske Veritas

Extreme value type-I distribution

Extreme value type-Il distribution

Extend Well Test

Joint Probability Density Function

Finite Element Method

First Order Reliability Method

First Order Second Moment Method

Iron Element

Floating Production System

Floating Production and Storage Offloading Vessels

Floating Production Semi-Submersibles

Gas Oil Ratio

Ultimate strength using Guedes Soares (1999)

Corrosion model and the Paik & Thayamballi (1997)

stiffened plate US formulation

Ultimate strength using Guedes Soares (1999)

Corrosion model and the Faulkner (1975) stiffened

plate US formulation

NOTATION-NOMENCLATURE AND ABBREVIATIONS

Abbreviations

ABS

AFOSM

API

Bbl

Bpd

BV

CG

CNS

COY

CPS

DCR

DNV

EV-I

EV-II

EWT

JPDF

FEM

FORM

FOSM

Fe

FPS

FPSO

FPSS

GOR

GPUS

PSR

PSF

PULS

PFEER

Hydrogen Element

Hasofer-Lind method

Health and Safety Executive

International Association of Classification Societies

Inner Bottom

International Maritime Organisation

Intergovernmental Panel on Climate change

International Ship and Structures Congress

Idealised Structural Unit Method

Joint Probability Density Function

Lloyd's Register of Shipping

Load and resistance factor design

Management and Administration Regulations

Maritime and Coastguard Agency

Marine Corrosion Forum

Microsoft

Monte Carlo Simulation

North Atlantic Oscillation

The Net Load of the section

Northern North Sea

Norwegian Petroleum Directorate

Oxygen Element

Outer Bottom

Probability Density Function

Ultimate strength using Paik et al. (2003) Corrosion

model and the Paik & Thayamballi (1997) stiffened

plate US formulation

Ultimate strength using Paik et al. (2003) Corrosion

model and the Faulkner (1975) stiffened plate US

formulation.

Pipeline Safety Regulations

Partial Safety Factor

Panel Ultimate Limit State

Prevention of Fire Explosion Escape and Response

H

H-L

HSE

lACS

ill

IMO

IPCC

ISSC

ISUM

JPDF

LR

LRFD

MAR

MCA

MCF

MS

MSC

NAO

NL

NNS

NPD

oOB

PDF

PPUS

PFUS

pH Potential of Hydrogen

RS Response Surface

RSM Response Surface Method

SLS Serviceability Limit State

SNS Southern North Sea

SORM Second Order Reliability Method

SOSM Second Order Second Moment Method

SRA Structural Reliability Analysis

SS Side Shell

SSC Ship Structure Committee

SWBM Still Water Bending Moment

IT Tvedt's Three Term Formula

TLP Tension Leg Platform

ULS Ultimate Limit State

UN United Nations

US Ultimate Strength

VB Visual Basic

VBM Vertical Bending Moment

VOC Volatile Organic Compound

VWBM Vertical Wave Bending Moment

WMO World Meteorological Organisation

Nomenclature

a

Definition)

a,ll1

The length of the plate or stiffener (Structural

B

The coefficient of thermal expansion (Thermal Stress)

The boundary conditions coefficients

The plate slenderness ratio (Structural Analysis)

The reliability (safety) index (Reliability Analysis)

The ship heading (Loads & Slamming)

The effective plate slenderness ratio

The Hasofer-Lind reliability index

The Euler's constant

The material factor

The permanent and variable action factor

The partial safety factor associated with the SWBM

The partial safety factor associated with the VWBM

The environmental action factor

The initial plate deflection

The initial stiffener deflection

The reduction of strength due to the weld induced

residual stress

The shift of neutral axis

The observed strain (Thermal Stress)

The spectrum broadness parameter (Loading Theory)

The strain of element i

The strain in any direction

The thermal strain

The yield strain

The yield tension block coefficient

The angle between vector curvature and x-axis

(Reliability Analysis)

The scale parameter (Loads)

PPPPePHLY

YM

Ys

~

Yw

Yw

&&s.J~

.JG

e

ee,

The ship heading angle (Loads)

The angle between an angular wave component and

the dominant wave direction (Loads)

The Smith correction factor

The stiffener slenderness (Structural)

The wave length rvv ave Loading)

The mean pulse arrival rate of the process Y;(t)

The uncertainty in ultimate strength bending moment

calculation

The uncertainty in the wave load bending moment

prediction

The mean duration of the pulses of Y;( t)

The mean of the SWBM.

The ship speed

The mean arrival rate of one load condition

The Poissson's Ratio

The mean arrival rate of one wave cycle

Stress (Thermal)

Stresses found by the uni-axial strain gages (Thermal)

8

8

K

J1swV

Vt

Vw

0;.

The elastic strength of the stiffened plate

The yield stress

The average stress of element i

The maximum stress

The material stresses of deck and outer bottom

The material yield stresses of inner bottom, upper side

shell and lower side shell

The proportional limit stress

The residual stress

The compressive plate welding stresses

The axial welding stresses in the stiffener

The ultimate strength of the stiffened plate

OJ

The standard deviation of the SWBM

The yield strength of the stiffened plate

The tensile yield strength of the vessel material

The cumulative density function of the standard

normal variate (Reliability Theory)

The partial safety factor associated with the resistance

of the structure

The strength of an unwelded plate

The load combination factor

The cumulative distributions function of the standard

normal variate

The average stress of element i at a strain of e;

normalized by yield stress

The frequency response function for the vertical wave-

induced bending moment for a homogeneously loaded

box shape vessel

Applied curvature (Code Formats)

The uncertainty as a result of non-linear load effects.

The uncertainty as a result of non-linear load effects.

Planes of reference

The uncertainty in ultimate strength

The uncertainty in wave load prediction

The load combination factor

The wave bending moment load combination factor

The still water bending moment load combination

factor

The wave frequency

OJO"y

Xnl

Xnw

Cl-C5

C

CJ, c.C

Cb,CB

Cw

Cx

Cy

The Gumbel parameter of the extreme SWBM

Accidental load parameter (Code Formats)

The (n-l )x(n-l) second derivative matrix (Reliability

Theory)

The cross-sectional area of one longitudinal stiffener

including associated full plating (Structural)

Total hull sectional area at deck, outer bottom and

inner bottom

The area of the flange

The sectional area of element iThe cross sectional area of the stiffener

The cross sectional area of the stiffener alone

Half of the total hull sectional area for side shell

including all longitudinal bulkheads

The total cross-sectional area

The area of the web

The sectional area of horizontal members at Y=Yi

The sectional area of vertical members at Z =Zj

The breadth of the stiffened panel

The stiffener spacing

The Weibull shape parameter (Statistical Theory)

The effective breadth (width) of the stiffened panel

The tangest effective width of the plate

The breadth of the stiffener flange

The vessel breadth

Structural test constants

The loading condition

The corrosion coefficients

Curvature

The block coefficient

The wave coefficient

Curvature over x-axis

Curvature over y-axis

asw

A

A

A

AI

Ai

As

Ast

As

At

AwAyi

A_zy

b

b

b

be'blB, e,

Fi

Corrosion wastage thickness

The design draught

The scantling draught

Thickness of the corrosion wastage at time t

Long-term thickness of the corrosion wastage

Corrosion rate

The density distribution function of still-water bending

moment in one year

The point-in-time distribution for load process [x}

The point-in-time distribution function for load

process [x]

Vector of differentiable processes (Gaussian and non-

Gaussian)

The depth of the vessel (Structural Analysis)

The failure domain (Reliability Definitions)

The nxn second derivative matrix of the limit state

surface in the standard normal space evaluated at the

design point (Reliability Theory)

The Young's Modulus of Elasticity (Structural

Analysis)

Environmental load parameter (Code Formats)

Specified frequent load parameter

Specified rare load parameter

The tangent modulus of element i

The tangent Young' modulus

The buckling flexural rigidity of the stiffener

The nonnormal cumulative density function of Xi

The nonnormal time variant cumulative density

function of XiThe probability density function of the extreme

SWBM

The nonnormal cumulative distribution function of Xi

d

ddesign

dscantd(t)

doo

d(t)fsw

!xir;

D

D

D

D

E

E

Ef

Ert:Et

Ele'

fi

fi(t)

Fsw The cumulative probability distribution of the extreme

SWBM

1

L

L

L

The inverse cumulative probability density distribution

of the extreme SWBM

The Froude number

The neutral axis

Permanent load parameter (Code Formats)

The shear modulus (Structural Analysis)

The performance function (Reliability Definitions)

Dead load parameter

Deformation load parameter

The instantaneous abscissa of the centroid

The instantaneous ordinate of the centroid

The height of the stiffener web

The shape parameter

The significant wave height

The moment of inertia of one longitudinal stiffener

including associated full plating (Structural Analysis)

The identity matrix (Reliability Theory)

Vector of rectangular wave renewal processes

Thermal Stress Coefficients

The skewness of the distribution (Slamming)

The wave number

The Weibull scale parameter (Statistical Theory)

The ith main curvature of the limit state at the

minimum distance point

The load combination factor related to the dynamic

bending moment arising from either slamming or

springing

The frame spacing

Subscript indicating lower part

The length of the ship

The load (Reliability Definitions)

The length between perpendiculars

Fn

g

G

G

G

I

I

J

k;

The scantling length.

The sectional added mass

Magnitude of the bending moment

The dynamic bending moment arising from either

slamming or springing

The characteristic bending moment resistance of the

hull girder calculated as an elastic beam

The magnitude of the bending moment in harbour

conditions in sagging and hogging

The maximum vertical wave bending moment in the

design life.

The component of moment about x-axis

The full plastic bending moment

The permissible still water bending moment in harbour

conditions

The characteristic design still water bending moment

based on actual cargo and ballast conditions

The most probable extreme still water bending

Lscant

M

MG

Mw.o

moment

Mw

The specified maximum still water bending moment

The long term most probable value of the SWBM as a

function of time

The still water moment

The total bending moment

The ultimate bending moment

The ultimate strength as a function of the time

dependent corrosion

The extreme vertical wave bending moment

The characteristic wave bending moment with annual

probability of exceedance of 10-2

The long term most probable value of the VWBM as a

function of time

The component of moment about y-axis

Ms.o

Mit)

MswMt

MuMit)

Mwe

rr

The first yield hull girder moments at deck and outer

bottom

The number of occurrences of each load condition

The number of peaks counted in the period reAxial forces in the x-, y-, z-direction

Co-ordinate system of reference

The probability of the most probable failure region

The peak factor

The probability of failure

The time variant probability of failure

The nominal probability of failure

The probability of the i'h failure regions

The joint probability of the th and r failure regions

Time dependent failure probability function

The degree of effectiveness of the CPS

Vector of stationary or ergodic sequences (Reliability

Formulation)

The applied loading (Reliability Definition)

Operational load parameter (Code Formats)

Short term load parameter

Long term load parameter

The characteristic shear resistance of the hull girder

calculated as an elastic beam

The characteristic design still water shear force based

on actual cargo and ballast conditions

The characteristic wave shear force with annual

probability of exceedance of 10-2

The radius of gyration of one longitudinal stiffener

including associated full plating

The effective tangent radius of gyration

The annualized corrosion rate (mm/year)

Vector of random variables (Reliability Formulation)

The resistance of the structure (Reliability Definition)

The rotation matrix (Reliability Theory)

PI

P

PIpit)

PfN

Pi

Pij

Pit)

q

Q

Qs

Qw

r

R

R

R

T

T

To

Tc

Telstarts

t;

The time variant resistance of the structure (Reliability

Definition)

The standard deviation of the relative vertical velocity

at the bow

Vector of not necessarily stationary random process

variables whose parameters depend on Q and/or R

(Reliability Formulation)

The load effect (Reliability Definition)

The seaway spectrum

The bending spectrum

The time variant load effect (Reliability Definition)

Time (years)

Thickness

Duration of a sequence of independently and

identically distributed random variables

The thickness of the stiffener flange

The lifetime of the structure

The thickness of the plating

The depth of corrosion wastage

The vessel draught (Principal Dimensions)

The random time of exit into the failure domain

(stochastic Processes

The age of the vessel (years) (Corrosion)

The temperature change (OC)(Thermal Stress)

The return period of the design life

The life of the coating (years)

The life of the CPS at which the general corrosion

R(t)

SVr

S

S

S;SBSet)

t

t

T

T

The time of exposure under the corrosion environment

in years

A uniform temperature experienced by an element

The average period

The instant at which the pitting corrosion starts

Xi

The duration of transition in years

The wave period

The corrosion accelerating life

The life of the structure or the time at which repair and

maintenance action takes place

The temperature of the water

The temperature of the air

The mode of the asymptotic extreme-value distribution

The Gumbel parameter of the extreme SWBM

Subscript indicating upper part

A standard normal process (Slamming)

The vessel's speed.

Coating life (years)

Transition time (years)

The distance of the centroid of element i to the

Uw

Usw

uuV

centerline

z

The horizontal distance of centroid of element i to the

instantaneous centre of gravity

The basic variables

A stochastic process

Coordinate indicating the position of horizontal

members above the base line

The distance of the centroid of element i to the

baseline

The vertical distance of the centroid of element I to the

instantaneous centre of gravity

The arbitrary-point-in-time value of lj

A sequence of independently and identically

distributed random variables

The neutral axis height

Coordinate indicating the position of vertical members

from a reference outer shell

The section modulus of a vessel

Xgi

Xi

X(t)

Y

Yi

Zo

Zj

Section modulus (the lesser of ZD and ZB)

Section moduli at deck and at outer bottom

Blank Page

CHAPTER!

INTRODUCTION

1.1 Introduction

One of the most familiar and fundamental concepts in engineering is that of a system, which

may be anything from a simple device to a vast multilevel complex of subsystems. A ship is

an obvious example of a relatively large and complex engineering system, and in most cases

the vessel itself is a part of an even larger system which influences with its behaviour, shape

and the economics involved in all the processes involved in building and maintaining such a

complex system. The ship consists of several subsystems, each essential to the whole

system such as the propulsion subsystem, and the cargo handling subsystem. The structure

of the ship can be regarded as a subsystem providing physical means whereby other

subsystems are integrated into the whole and given adequate protection and suitable

foundation for their operation. In general terms the design of an engineering system may be

defined as:

"The formulation of an accurate model of the system in order to analyze its

response-internal and external-to its environment, and the use of an

optimization method to determine the system characteristics that will best

achieve a specified objective, while also fulfilling certain prescribed

constraints on the system characteristics and the system response."

1.2 Rationally-Based Structural Design

The ever increasing demand for more efficient marine transport has lead engineers in that

field to consider a number of significant changes in ship sizes, types and production

methods over the last 40 years. Different types of vessels have appeared attempting to meet

the demands of the shipping industry. The growing number of factors which give rise to this

process of change The need for protection against pollution, new trade patterns that emerge,

new types of cargos and the need to safely transport any type that might be considered

dangerous, increasing numbers in production lines of standard ship designs and their

consequent development to achieve a higher degree of efficiency and the development of

structures in vehicles for the extraction of ocean resources, require scientific, powerful and

versatile methods for structural design. One can say that we are at present in the midst of a

Moatsos, I. 2005

Chapter l.Introduction 38 II

Based on individual ship designer and shipyard experience and ship performance, in the

past ship structural design had been mostly empirical based on the structural designers'

accumulated experience This approach lead eventually to the publication of structural

design codes, or "rules" as they are referred to in the industry, published by various ship

classification societies. These "manuals" of ship structural design provided a simplified and

care-free method for the determination of a ship's structural dimensions. This procedure

provided a time and cost effective method for design offices and simplified classification

and approval process at the same time. The method unfortunately has several disadvantages

including the inability to handle the large number of complex modes of structural failure,

the possibility of unsuitable results in regard to the specific goals of the ship owner or the

particular purpose or economic environment that the ship is required to operate in and the

inability to distinguish between structural adequacy and over adequacy leading to increased

cost and steel weight in a structure. Most important though is the large number of

simplifying assumptions included which bound such design process within certain limits.

progressive and gradual but profound change m the philosophy and practice of ship

structural design.

For these reasons there is a trend within the shipbuilding and ship design industry and the

academic institutions involved in research related to these fields toward "rationally-based"

structural design, which may be defined according to Hughes (1983) as:

"Design which is directly and entirely based on structural theory and computer-

based methods of structural analysis and optimization, and which achieves and

optimum structure on the basis of a designer-selected measure ofmerit"

Thus rationally-based design involves a thorough and accurate analysis of all the factors

affecting the safety and performance of the structure throughout its life, and a synthesis of

this information, together with the goal or objective which the structure is intended to

achieve, to produce that design which best achieves the objective and which provides

adequate safety. This process involves far more calculation, but that can be more than offset

by using computers. For this reason rationally-based structural design is necessarily a

computer-based, semi-automated design process.

One of the most significant trends in the design of marine structures is the ongoing shift

from deterministic to probabilistic bases for design. In deterministic design, the engineer

Moatsos, I. 2005

Chapter l.Introduction 39

selects a load which he considers to be on the high side of the loading spectrum, and a

design strength approach which he feels will be conservative, thus underestimating actual

strength, and then just to be safe may add a factor of safety on either or both sides to cover

any shortcomings in his analysis. Coupled with thousands of ship-years of experience and

extensive investigations after casualties, this approach usually leads to a successful design.

Yet with every success, the designer never knows how close he came to failure, and with

each failure, he never knows how close he came to success. And with a failure, particularly

the ones that lead to loss of the ship, it is nearly impossible to trace the failure to a design

flaw, material imperfections, weak inspection, poor maintenance, imprudent seamanship,

improper loading, freak environmental conditions, or a number of other factors individually

or combined. The probabilistic approach provides another dimension to the safety analysis

by associating with each event a joint probability of success, or conversely, of failure. This

presumably permits the designer, the builder, the Class, owner and all concerned regulatory

bodies to determine how close a successful design will come to failure, but it does not

guarantee success.

1.3 ReliabilityBased Code Formats

Over the past several years, there has been an increasing trend toward the implementation of

structural reliability theory in the development of design codes for marine and other types of

structures. The trend to reliability based approaches to design takes into account some

important considerations resulting from research and experience such as:

1. The advantages of specifying and designing for, a certain level of safety or

reliability over an entire structure.

2. The importance of limit-state-failure approach to design, as distinct from a purely

working-stress approach.

3. The statistical nature and especially the randomness of the design variables

associated with both loading and resistance ..

A reliability approach to design, based on the above consideration, provides the opportunity

to better quantify the "safety" of a particular marine structure, and also to establish a more

direct relationship between design, redundancy and inspection. The reliability approaches

which have been investigated and have been widely published to date have generally been

Moatsos, I.2005


based on Level-II first-order second moment methods mostly. A major aspect of these

methods is the concept of a reliability or safety index fl, which is related to the notional

probability of failure and thus is a measure of the safety of a particular design. Once a target

reliability index is established for a structure, and the design variables associated with

loading and strength are represented in a realistic statistical manner, appropriate "partial

safety factors" are derived from use in a limit-state safety-check equation which relates

extreme loading to strength of the specific limit state. In this manner, design is directly

related to a specified level of reliability or safety, and some of the inherent and subjective

uncertainties in load predictions and as-built structural conditions are better defined and

properly taken into consideration. Thus, the reliability concept can be used to improve

structural performance for a marine structure, thereby enhancing the structure's ability to

fulfil its design purpose. Since a limit-state approach to design is inherent in reliability

methods, the subject of redundancy can be more directly addressed and quantified than in

traditional working stress approaches. Also it may be possible to establish quantitative

trade-offs between the safety level and redundancy. For example, the target reliability p, andcorresponding partial safety factors, could be directly related to the degree of redundancy

available. Thus, a highly redundant structural component could be assigned a lower (more

liberal) target fl than its no redundant counterpart, all other aspects being equal. The

potential also exists for using structural reliability theory in the design stage to determine

the required level of redundancy for an overall structural system, although this is an area

requiring further development.

In the same manner that options are available for relating design to redundancy in a

reliability-based approach, this interrelation could also include consideration involving

inspection and repair capabilities. That is, the quantitative trade-offs possible between target

reliability and level of redundancy could be expanded to include consideration of such

factors as accessibility of structural components for in-service inspections, dependability of

proposed inspection techniques, difficulty and cost repair, etc.

Similar to the structural resistance, a more realistic representation can also be extended to

the load effects in the reliability approach. The environmental loadings of a marine

structure, particularly of a floating offshore structure, such as wind, wave current and tide

are random in nature. Therefore, it is essential to have a proper statistical description of

Moatsos, I. 2005

Chapter l.1ntroduction 41

these random events in predicting load effects.· Often, it requires knowledge of the

multivariate joint probability distribution for the simultaneous occurrence of all correlated

and uncorrelated environmental parameters. For each event, loading and structural response

are computed, and then these responses are weighted according to the probability of

occurrence of each environmental event. Applying order statistics, for instance, the most

probable value or extreme value of loading and load effects can be predicted in conjunction

with probability level of exceedance. Based on the distribution of these extreme values, a

set of corresponding partial safety factors with respect to various load components can be

derived.

In various recent guidelines and regulations by various statutory and regulatory bodies, the

semi-probabilistic method has been chosen as the common basis for steel and concrete

structural design. However, the crux of the matter does not mainly depend on the method as

such, but on the proper definitions of the relevant limit states and the associated partial load

and material safety factors. The four limit states generally applied in such guidelines can be

found in the appendix (Table 1.1). A more detailed view of some of the approaches is

required to discuss the most current developments in some of the International Standards

published for Marine Structures and the extent to which some of the current ship and

offshore regulations have assimilated Structural reliability Analysis (SRA) techniques and

the Ultimate Limit State as equivalent measures of structural safety compared to traditional

methodology. In certain cases the way that loads are combined is described but also how

uncertainties in associated variables are considered. The principal international standard for

offshore structures is ISO 13819-1 (ISO 2005): General requirements, which also will be

published as a European standard EN-ISO 13819-1(ISO 2005). Information about actions

and action effects can be found in the related standards, ISO 13819-2 (ISO 2005).

1.3.1 CSAOffshore Structures Code

The CSA Offshore Structures Code was developed during the late 1980s, and was

subsequently adopted in the early 1990s. These Standards have been used in Canada and

elsewhere, particularly because of their treatment of extreme environments; i.e. sea ice,

icebergs, and combinations of them with other environmental factors such as waves and

earthquakes. The CSA Offshore Structures Code (2004), as described by Frederking et al.

(2004), uses limit states design procedures to accommodate the uncertainties in the

Moatsos, I. 2005

Chapter l.1ntroduction 42

environment and associated loads, as well as uncertainties in structure resistance. The

fundamentals of the approach are set out in the S471 Standard (CSA, 1992). The design

approach of the Standard defines two limit states:

• Ultimate limit states: limit states concerned with safety of life and environmental

protection.

• Serviceability limit states: those that restrict the normal use or occupancy of the

structure or affect its durability.

There is a further definition of two safety classes of the ultimate limit state for verifying the

safety of the structure or any of its structural elements:

• Safety Class I: for loading conditions where failure would result in great risk to life

or a high potential for environmental damage.

• Safety Class 2: for loading conditions where failure would result in small risk to life

and a low potential for environmental damage.

To meet the design objectives for safety, target reliability levels have been established that

were subsequently used for calibrating the design limit states. The target reliability levels

selected are outlined in the appendix (Table 1.2). Other standards set similar reliability

levels, e.g. NORSOK (1999) and the Joint Committee on Structural Safety (2001). The CSA

Standard and the noted standards use an annual probability of failure rather than a return

period.

Reliability considers the uncertainty of loads, environmental and other, as well as the

resistance or strength of the structure. Design to the prescribed reliability levels requires

partial factors for both loads and the resistance. The values of the partial factors were

calibrated for various loads and load combinations in a series of studies that are mentioned

in Frederking et al. (2004). In addition to general requirements for design, the Standard

provides guidance on describing environment conditions and the use of environmental

parameters in determining environmental loads and load combinations. The load

combinations and load factors are presented in abbreviated form in the appendix (Table

1.3). The 2004 edition of S471 contains extensive guidance notes on the use of the table

Moatsos, I. 200S

Chapter l Jntroduction 43

(Table 1.3) and the guidelines should not be used without reference to the whole Standard.

Load parameters include Permanent G, Dead GD, Deformation GR, Operational Q, Short-term Qj, Long-term Q2, Environmental E, Specified frequent Ej. Specified rare Er, and

Accidental A.

1.3.2 NORSOK Standards

The NORSOK standards are developed by the Norwegian petroleum industry as a part of

the NORSOK initiative and are jointly issued by OLF (The Norwegian Oil Industry

Association) and TBL (Federation of Norwegian Engineering Industries). NORSOK

standards are administered by NTS (Norwegian Technology Standards Institution). Their

purpose is to replace the individual oil company specifications for use in existing and future

petroleum industry developments, subject to the individual company's review and

application. The standards make extensive references to international standards and specify

general principles and guidelines for determination of actions and action effects for the

structural design and the design verification of structures. The standard is applicable to all

types of offshore structures used in the petroleum activities, including bottom-founded

structures as well as floating structures and is also applicable to the design of complete

structures including substructures, topside structures, vessel hulls, foundations, mooring

systems, risers and subsea installations and to the different stages of construction (namely

fabrication, transportation and installation), to the use of the structure during its intended

life, and to its abandonment. Combinations of environmental actions can be found in

Section 6.7 of N003 (NORSOK 1999), and combination of accidental actions can be found

in Section 8.7 of NOO3(NORSOK 1999). In the appendix (Table 1.4) demonstrates a

summary of characteristic actions and combinations as described by the standard.

A part of it the standard also makes provision for taking into account temperature effects on

the structure designed as a result of the variability of air and sea temperature levels in the

North Sea. According to the standard structures shall be designed for the most extreme

temperature differences they may be exposed to. This for instance applies to:

• Storage tanks.

Moatsos, l.2005


• Structural parts that are exposed to radiation from the top of a flare boom. One hour

mean wind with a return period of 1 year may be used to calculate the spatial flame

extent and the air cooling in the assessment of heat radiation from the flare boom.

• Structural parts that are in contact with pipelines, risers or process equipment.

The ambient sea or air temperature is calculated as an extreme value with an annual

probability of 10.2, unless more accurate measurements or calculations are carried out, air

and sea temperatures may be taken from according to the appendix (Fig. I. I). Sea

temperature also varies with depth. The local air temperature may be higher as a result of

sun radiation. During fabrication of the structure, all dimensions should be related to a

reference temperature. Eriksred and Adlandsvik (1997) give data for sea temperatures at the

sea floor that can be used in an early design phase.

According to NOO4 the hull girder strength shall be evaluated for relevant combinations of

still water bending moment and shear force, and wave induced bending moment and shear

force. The wave-induced bending moments and shear forces shall be calculated by means of

an analysis carried out utilising the appropriate statistical site specific environmental data.

Relevant non-linear action effects shall be accounted for. The following design format shall

be applied:

(1.1)

(1.2)

where MG is the characteristic bending moment resistance of the hull girder calculated as an

elastic beam; Ms is the characteristic design still water bending moment based on actual

cargo and ballast conditions; Mw is the characteristic wave bending moment with annual

probability of exceedance of 10.2; QG is the characteristic shear resistance of the hull girder

calculated as an elastic beam; Qs is the characteristic design still water shear force based on

actual cargo and ballast conditions; Qw is the characteristic wave shear force with annual

probability of exceedance of 10.2; YM is the material factor; Ys is the permanent and variable

action factor and rw is the environmental action factor. The action factors shall be in

accordance with the Norwegian Petroleum Directorate (NPD), (Table 1.5).

Moatsos, I. 2005

Chapter Llntroduction 45

For combination of actions an action coefficient of 1.0 shall be applied for permanent

actions where this gives the most unfavourable response. The action coefficient for

environmental actions may be reduced to 1.15 in action combination b, when the maximum

still-water bending moment represents between 20 and 50 % of the total bending moment.

This reduction is applicable for the entire hull, both for shear forces and bending moments.

1.3.3 JCSS Probabilistic Model Code

The JCSS Probabilistic model code was written with fixed structures in mind and not

necessarily marine structures but the safety levels and techniques described within are

commonly applied to marine structures. Target reliability values are provided within the

Code and they are based on optimization procedures and on the assumption that for almost

all engineering facilities the only reasonable reconstruction policy is systematic rebuilding

or repair. Target reliability values for ultimate limit states are proposed in the appendix

(Table 1.6). and are obtained based on cost benefit analysis for the public at characteristic

and representative but simple existing structures and are compatible with calibration studies

and statistical observations.

The shadowed value (Table 1.6) should be considered as the most common design situation.

In order to make the right choice in this table a classification into consequence classes based

on the ratio p is used. The ratio is defined as the ratio between total costs (Le construction

cost plus direct failure costs) and construction costs.

• Class 1Minor Consequences: p is less than approx. 2

Risk to life, given a failure is small to negligible and economic consequences are

small or negligible (e.g. agricultural structures, silos, masts)

• Class 2 Moderate Consequences: p is between 2 and 5

Risk to life, given a failure, is medium or economic consequences are considerable

(e.g. office buildings. industrial buildings. apartment buildings)

• Class 3 Large Consequences: p is between 5 and 10

Moatsos, I. 2005

Chapter l.lntroduction 46

Risk to life, given a failure, is high, or economic consequences are significant (main

bridges, theatres, hospitals, high rise buildings)

If P is larger than 10 and the absolute value of H is also large, the consequences should be

regarded as extreme and a full cost benefit analysis is recommended. The conclusion might

be that the structure should not be built at all.

According to the code in terms of the Serviceability Limit State (SLS), when setting targets

for SLS it is important to distinguish between irreversible and reversible SLS. Target values

for SLS can be derived based on decision analysis methods. For irreversible SLS tentative

target values are given in the appendix (Table 1.7). A variation from the target serviceability

indexes of the order of 0.3 can be considered for reversible SLS no general values are given.

1.3.4 BV Rules for the Classification of Ships

In 2001 Bureau Veritas (BV) was the first Classification Society to incorporate in its

Regulations for the Classification of Steel Vessels Ultimate Limit State checks for the

design of marine structures through a detailed algorithm described in details in the

published standards. Its requirements applying to ships equal to or greater than 170 m in

length also include partial safety factors developed through reliability analysis and code

calibration. The partial safety factors to be considered for checking the ultimate strength of

the hull girder are specified in the appendix (Table 1.8).

The bending moment in navigation M and harbour conditions MH, in sagging and hogging

conditions, considered in the ultimate strength check of the hull girder, is obtained, in kNm,

from the following formulae:

M = YSIM sw + YWIM wv

MH =YsIMp.H +O.lYwIMwv

(1.3)

(1.4)

where Mp.H is the permissible still water bending moment in harbour conditions, at any hull

transverse section in harbour conditions, in hogging or sagging conditions and is obtained,

in kN.m, from the following formula:

Moatsos, I. 2005


(1.5)

where ZA,M is the lesser of ZAB and ZAD as defined by the rules in a procedure similar to such

suggested by IACS and followed by all major Classifications societies worldwide.

The bending moment in sagging and hogging conditions, to be considered in the ultimate

strength check of the hull girder, is obtained, in kNm, from the following formula:

(1.6)

The ultimate bending moment capacities of a hull girder transverse section, in hogging and

sagging conditions, are defined as the maximum values of the curve of bending moment

capacity M versus the curvature X of the transverse section considered (Figure 1.2). The

curvature X is positive for hogging condition and negative for sagging condition and the

curve M-X is to be obtained through an incremental-iterative procedure.

The hull girder transverse sections are constituted by the elements contributing to the hull

girder longitudinal strength, considered with their net scantlings. As it can be seen in the

appendix (Figure 1.3) each step of the incremental procedure is represented by the

calculation of the bending moment M, which acts on the hull transverse section as the effect

of an imposed curvature Xi.

It is to be checked that the hull girder ultimate bending capacity at any hull transverse

section is in compliance with the following formula:

(1.7)

Mu is the ultimate bending moment capacity of the hull transverse section considered, in

kNm where in hogging conditions Mu =MUR and in sagging conditions Mu =Mus; MUR the

ultimate bending moment capacity in hogging conditions; M us the ultimate bending moment

capacity in sagging conditions and M the bending moment, in kNm.

Moatsos, I. 2005


1.4 Discussion-Remarks

Although the general approaches that has been proposed so far, and that will be described in

detail in the subsequent chapters of this thesis, for the calculation of the ultimate strength

(bending moment) of the hull girder appear to be valid, there are various complicating

factors which introduce element of uncertainty into the process. These include:

• The possible effects of corrosion

• The presence of lateral pressure on some hull elements

• Imperfections in the as-built structure, including both geometrical and residual stress

defects

• The influence of finite element modelling

Despite such uncertainties and by maintaining consistent assumptions (Thayamballi, Chen

& Chen, 1987) ultimate strength analysis can lead to useful conclusions for the purposes of

design assessment, and for indicating usage factors and safety margins implicit in design

codes. It can thus be concluded that hull strength analysis, though not yet a regular part of

ship structural design is becoming accepted as a potentially valuable part of that process.

The essential requirement, therefore, in evaluating ultimate hull bending strength is an

ability to predict moment-curvature relationships and any investigation of the strength of the

hull girder for design purposes should incorporate such relationships.

Recent trends in the regulatory development of regulatory frameworks for marine structures

(Moatsos and Das 2004, Moatsos and Das 2005) signify that the volume of research in the

development of approaches and methodology for reliability analysis will increase in the

near future reliability based code formats will become even more popular for marine

applications.

There is an increasing tendency to adopt a "goal-based" approach to regulation in general

and there are good technical and commercial reasons for believing this approach is

preferable to more prescriptive regulatory approaches. This trend is very apparent in recent

developments at the International Maritime Organisation (IMO) whose purpose is to

develop and control worldwide maritime safety legislation. The key elements of the safety

Moatsos, I. 2005


philosophy behind "goal-based regulation" at IMO (ARGOS et al. 2005) include a rational

set of safety goals and consistent definitions of functional requirements to be compiled with

by ship design and construction rules and best-practice codes developed by Classification

Societies, among others. However a mechanism to verify such compliance is still missing

from the modem regulatory regime.

The need exists for the development of more detailed approaches that will not only

accurately model the variety of extreme conditions encountered by current and future

developed marine structures, but will also not prohibit innovative solutions and provide the

basis upon which modem regulatory approaches can develop without following a strict

prescriptive approach. This study aims to propose such an approach for FPSOffanker type

of marine structures by using a variety of existing formulations and combining them in a

unique way, so as to examine the best possible way to perform such an analysis and study

the effects of a variety of extreme conditions encountered by vessels already in operation.

Moatsos, I. 2005


Chapter 1, References:

TheAmerican Bureau of Shipping Website [Online. Internet.] Available:http://www.eagle.org! , Accessed: 1 Jun, 2005.

ARGOS, RINA, MCA, SSRC & PRS 2005, "GOALREG: Development of Goal BasedRegulations for Ship Design, Construction and Operation", EU 6th FrameworkProgramme Project Proposal.

ASRANet Networkfor Integrating Structural Analysis, Risk and Reliability Website [Online.Internet.] Available: http://www.asranet.com!. Accessed: 1 Jun, 2005.

BV Rules for the Classification of Steel Ships 2004, Part B Chapters 5 and 6, BureauVeritas, France, January 2004.

CSA 2004, "S471-04 General requirements, design criteria, the environment and loads"Published as a National Standard of Canada, Canadian Standards Association, Ontario,Canada.

CSA 1992, "CAN!CSA-S47i-92 General requirements, design criteria, the environment andloads", Published as a National Standard of Canada, Canadian Standards Association,Ontario, Canada.

Det Norske Veritas Website [Online. Internet.] Available: http://www.dnv.com!. Accessed:1 Jun, 2005.

Eriksred, G., Adlandsvik, B. 1997, "Bottom Temperatures along the Mid-NorwegianShelf', Havforskningsinstituttet, Bergen.

Frederking R., Brown T., Grant R. 2004, "Updating the Canadian Standards AssociationOffshore Structures Code", Proceedings of the Fourteenth International Offshore andPolar Engineering Conference ISOPE 2004, Toulon, France, May 23-28.

Hughes, O.F. 1983, Ship Structural Design, A Rationally Based, Computer Aided,Optimization Approach, John Wiley and Sons, New York.

International Association of Classification Societies Website [Online. Internet.] Available:http://www.iacs.org.ukl , Accessed: 1 Jun, 2005.

International Organization for Standardization Website [Online. Internet.] Available:http://www.iso.org! ,Accessed: 1 Jun, 2005.

International Maritime Organisation Website [Online. Internet.]http://www.imo.org! , Accessed: 1 Jun,2005.

JCSS Probabilistic Model Code 1999, The Joint Committee on Structural Safety, 12th Draft

Available:

Lloyd's Register Website [Online. Internet.] Available: http://www.1r.org/ , Accessed: 13Jun,2005.

Moatsos, I., Das, P.K. 2004, "Structural Reliability Framework for FPSOsIFSUs: Phase I",UK Health and Safety Executive (HSE) Report 261 Project D4007, HSE Books, ISBN0717628906, London, UK.

Moatsos, I., Das, P.K. 2005, ''''Structural Reliability Framework for FPSOsIFSUs: PhaseII", UK Health and Safety Executive (HSE) Report Project R34.011, HSE Books,London, UK.

NORSOK Standards 1999. "Actions and Action Effects N-003", Norwegian TechnologyStandards Institution.

Moatsos, I. 2005

http://www.eagle.org!

http://www.asranet.com!.

http://www.dnv.com!.

http://www.iacs.org.ukl

http://www.iso.org!

http://www.imo.org!

http://www.1r.org/


NORSOK Standards 1998, "Design of Steel Structures N-004'', Norwegian TechnologyStandards Institution.

Ship Structure Committee Website [Online. Internet.] Available:http://www.shipstructure.org/. Accessed: 10 Jun, 2005.

Thayamballi, A.K., Chen, Y.K., Chen, H.H. 1987, "Deterministic and Reliability BasedRetrospective Strength Assessment of Oceangoing Vessels", Transactions of the Societyof Naval Architects and Marine Engineers (SNAME).

The Joint Committee on Structural Safety Website [Online. Internet.] Available:http://www.jcss.ethz.ch/. Accessed: 20 May, 2005.

Moatsos, I.2005

http://www.shipstructure.org/.

http://www.jcss.ethz.ch/.


Appendix 1, Figures

Figure 1.1 (Left) Highest and lowest air temperature with an annual probability of exceedance of 10-2 •

(Middle) Highest surface temperature in the sea with an annual probability of exceedance of 10-2•(Right) Lowest surface temperature in the sea with an annual probability of exceedance of 10-2• The

temperatures are given in degrees Celsius. (NORSOK N003, 1999).

M

--~--------~~--------~-+XXF

Sagging condition

Figure 1.2.Curve bending moment capacity M versus curvature X(DV, 2004).

Moatsos, L 2005

Chapterl.Introduction 53

Cs.lculatioo a lne srain [. induced an eachslrudural elemertt by the rul\fature Xi

ionhe net!'!ral ax is position Nhl

Foream sru::tural element.; calatf.atiiooat the oS!r;:;ss{Jrele.lant to 1h;:; slrain E. (.----11>1

Calcul81ion d !he nel\' pDStioo cd thenerJi:ral axis ~ .impo~ the equifbium

00 the Slress resultant F

'-----NO

YES

YES

C\a!oofatiioo at the bentt."Ig moments M.refelsm tothe curvature Xi ISIUlmming the

COCltrlbutioo of ead'l ttroo· ral ~ement stress

L-------------------NOYES

~

Figurel. 3. Flow chart of the procedure for the evaluation of the curve M-x. (RV, 2004).

Moatsos, 1. 2005


Appendix 1, Tables

Limit States of Design Main Characteristics

Ultimate Limit State (ULS) Ultimate load carrying capacity

Rupture or yielding of sections

Collapse or instability of single members of

structure

Transformation into mechanisms

Loss of Equilibrium, etc.

Fatigue Limit State (FLS) Accumulated effects caused by cyclic or

repeated stresses during service life

Disintegration caused by accumulated

fatigue damage

Insufficient residual strength

Progressive Collapse Limit State (PLS) Accidental loss or overloading of single

members may render the structure or major

parts thereof into a condition where

progressive failure may take place

Serviceability Limit State (SLS) Specifications as regards serviceability or

durability

Excessive deformations (vibrations) without

loss of equilibrium

Damage caused by corrosion

Aspects of durability in the general sense,

including unforeseen amount of maintenance

and repair

Table 1.1 Design Limit States considered by statutory and regulatory bodies worldwide.

Moatsos, 1. 2005

Chapter Llntroduction 55

Safety Class Consequence of Failure Target AnnualReliability Level(reliability = 1 - PO

Safety Class 1 Great risk to life or a 0.99999 = (1- 10.5)high potential forenvironmental damage

Safety Class 2 Small risk to life and a 0.999 = (1- 10.3)low potential forenvironmental damage

Serviceabil ity Impaired function 0.9 = (1- 10.1)

Table 1.2 Safety Classes and Reliability Levels (Frederking et al., 2004).

Load Load factorscombination

ultimate limit states - Safety Class 11 125 Go.+ Ott+ 1.45 QriJ-12 <l2+ 0.7 Er2 125 Go.+ Ott + 1.15 Qt+ 1.7 <l2+0.7 Er3 1.05 Go.+ Ott + 1.15 Ql+ 1.35 Er4 1.05 Gn +Ott + 1.15 Ql+ s,5 1.05 Gn + G. + L15 O!+ A

6damaged (1.05 or 0.9) 0;.;+-~ +Q1+Erultimate limit states - Safety Class :2

7 1.05 Go +Gx. + 1.1Q1+ 0.7502 + 0.85 Er8 1.05 Gn + Ott + 0.9 Ql+ 1J .~ + 0.85 Er9 1.05 CiD + Ga + 0.9 Ql+.Er

10damawi (LOS or 0.9) Go + Ott+ Ql+ O.7 ~Ultimate limit states - Fati2Ue

11 Go.+Gx.+~+ErServiceabilitv limit states

12 Gn+~+o,+0.7&

Table 1.3 Load factors and load combinations (Frederking et al., 2004).

TEMPORAlty (O}'1>mONS NORMAL OPERATIONS

Sc\-n~ Fmp t;'bl~. IA=demll=it m~ S.",iculW.ity F.n,...Dmit LlIiwa. Dmit kcmDbllimit mtelimit UIbI hmit_ hmit_ AbDOnllO! D~ Iimit_ ute 0U1a AOa!mml ~

.&ot <ODditiom .f!'.oct conditic>Olp~actiom EXPECTED VALL"!!V..,.ble_tico>.al SPECIFlED VAllJEaeti<u;

A=uolCr."_ DopeadaI- bpoded Dopeudat ... Expeded A=uol A=uol pmb.ability of

....ut ope2umW - Volue d..poDdmJI .......... .,,_ tIk ... opor.IbOI1>l JC'licol probability of ..... bability of _eedimee

IdIODS ~ hUtoay teqWnIDI!I>IS m.uxy .~ ~ -ur'_104 -1c;4

lHfDnu.tIaDactiom EXPECTED EXTREME VALL"E

A=uol

kc:ia.-! Not oppIiable ~ Not oppIiable pn>bability of Not oppljcableIdIODS GIl ~.-- .IO~

w-

Table 1.4 Characteristic Actions and Combinations (NORSOK N003, 1999).

Moatsos, L 2005


Action 1s 1wcombinations

a 1.3 0.7b 1.0 1.3

Table 1.5 Load Action Combinations (NORSOK N004, 1998).

1 2 3 4Relative cost of Minor Moderate Large consequencessafety measure consequences of consequences of of failure

failure failureLarge (A) 6=3.1 (Pr-10·3) 6=3.3 (pr-lOA) 6=3.7 (pr-10·4)Normal (B) 6=3.7 (pr-1O.3) ~=4.2 (PF10-5) 13=4.4(Pr- 10.5)Small (C) 6=4.2 (pr-10·3) 6=4.4 (pr-10·6) 6=4.7 (Pr-1O·6)

Relative Cost of Safety Measure Target Indexes (irreversibleSLS)

High 6=1.3 (Pr-lO·I)Normal 6=1.7 (Pr-S 10.2)Low 6=2.3 (pr-lO·2)

Table 1.6 Tentative target reliability indices p (and associated target failure rates) related to one yearreference period and ultimate limit states. (JCSS, 1999).

Table 1.7 Target reliability indices (and associated probabilities) related to one year reference periodand irreversible SLS (JCSS, 1999).

Partial safety factor covering Symbol Valueuncertainties on:

Still water hull girder loads YSI 1,00

Wave induced hull girder loads YWI 1,10

Material YM 1,02

Resistance YR 1,03

Table 1.8 Partial safety factors (BV, 2004).

Moatsos, 1. 2005

CHAPTER2

GLOBAL WARMING AND THE CLIMATE CHANGEPROBLEM

2.1 Introduction

The 2003 heatwave in Europe that killed at least 20,000 people and triggered losses of an

estimated £7bn could represent the future behaviour of our climate, according to research

reported in the Guardian (2004). Climate scientists from Zurich have reported in Nature

online (2004) that the summer heat-wave that broke all records in France, Germany and

central Europe had been extremely unusual, even given the steady rise in average global

temperatures over the past 150 years. Swiss researchers used computer-driven weather

models to determine whether climate variability, the already large difference between

weather extremes, was likely to increase with average temperature and growing

concentrations of greenhouse gases. In one simulation they found that, towards the end of

the century, every second summer could be as hot and as dryas 2003.

2.2 Global Warming & Statements on Future Climate

In December 2002 and March 2003 the World Meteorological Organisation (WMO) issued

a number of statements in the form of press releases concerning the status of global climate

(WMO 2002) in 2002 and concerns over the future of our climate (WMO 2003). According

to the WMO statements and the relevant published research the global mean surface

temperature for 2002 is expected to be approximately 0.50 °C above the 1961-90 annual

mean value, according to records maintained by Members of the World Meteorological

Organization (WMO). Consequently, 2002 will supplant 2001 as the second warmest in the

instrumental record. The warmest year in the 1860 to present record for land and sea surface

areas remains 1998. The ten warmest years have all occurred since 1987, nine since 1990.

While the trend toward warmer globally averaged surface temperatures has been uneven

over the course of the last century, the trend for the period since 1976 is roughly three times

that for the past 100 years as a whole (Fig. 2.1). The rise in global average surface

temperatures since 1900 now exceeds more than 0.60 C (Fig. 2.1) where the solid curves

have sub-decadal time-scale variations smoothed with a binomial filter. Sea surface

temperature anomalies across much of the land and sea surface of the globe in general

Moatsos, I. 2005

Chapter 2.Glohal Climate Change 58

contributed to the near record temperature ranking for the year. Recent occurrences extreme

weather- and climate-related events could well be glimpses of what a change in climate

could bring upon us. According to the WMO statements and research reports, the future cost

of inaction to protect climate is expected to exceed by far the cost of timely action.

Climate change will force temperatures up and precipitation down across the Scottish

islands over the next 100 years, according to research published by the Hadley Centre

(British-Irish Council 2003). While the summers wi1l be drier, the winters wi1l be wetter

says the report prepared for the British-Irish Council using computers at the Hadley Centre

for Climate Prediction and Research, part of the UK Meteorological office. By the year

2100, annual average temperatures will increase across the Western Isles, the Orkney

Islands and the Shetland Isles according to the report, which is based on four contrasting

scenarios of future greenhouse gas emissions derived from the work of the

Intergovernmental Panel on Climate Change (lPCC). The authors attach a "relatively high

degree of confidence" to the main trends described in the study. But they admit to scientific

uncertainties associated with the climate change scenarios, as a result of the level of

uncertainty of how levels of greenhouse gas emissions will change in the future. For the

medium-high scenario of future emissions, annual temperatures could rise by 1.8 degrees

Celsius (3.24 degrees Fahrenheit) for the Western Isles, 2 degrees C (3.6 degrees F) for the

Orkney Islands, and 2.2 degrees C (3.96 degrees F) for the Shetland Isles. Perhaps most

alarmingly, the report admits that we do not understand much about the Gulf Stream and the

related ocean currents that bring warm water to the west coast of Scotland, but it is

predicted to lose 20 percent of its strength over the next 100 years. The frequency and

severity of storms will increase, the report predicts, threatening coastal communities and

wildlife habitats with flooding. More unpredictable weather could add nearly half a meter,

or about 20 inches, to high tide levels in the worst storms.

Weather anomalies are a global phenomenon these days (Fig. 2.2) which can occur during

any season and take a large number of different shapes ranging from tropical storms in the

middle of winter to hurricanes and gale force winds in the middle of summer. The

meteorological community has developed a number of tools for modelling weather

phenomena (Fig. 2.3) such as the ones used by the Hadley Centre and the Met Office in the

UK. As it can be seen from the figure an average diurnal change in temperature can easily

be in the region of 10°C, especially during the summer months.

Moatsos, I. 2005

Chapter 2.Global Climate Change 59

The way that climate change will affect us in the next 20 years may go as far as to become a

matter of national security according to The Observer (2004). In articles published recently

according to reports commissioned by the US Department of Defence and the Pentagon,

Climate change over the next 20 years could result in a global catastrophe costing millions

of lives in wars and natural disasters as the document predicts that abrupt climate change

could bring the planet to the edge of anarchy as countries develop a nuclear threat to defend

and secure dwindling food, water and energy supplies. The threat to global stability vastly

eclipses that of terrorism according to the report and is clearly stated that it was already

possibly too late to prevent a disaster happening as it is unknown exactly where we are in

the process. It could start tomorrow and we would perhaps not know for another five years.

More specifically:

• Between 2010 and 2020 Europe will be hardest hit by climatic change with an

average annual temperature drop of 6degrees Fahrenheit. Climate in Britain might

become colder and drier as weather patterns begin to resemble Siberia.

• By 2010 the US and Europe might experience a third more days with peak

temperatures above 90 degrees Fahrenheit. Climate could possibly become an

'economic nuisance' as storms, droughts and hot spells create havoc for farmers.

It may all sound like a script coming from a science fiction film but unfortunately, and most

worryingly, these are issues that are in discussion not only within Scientific groups as a

matter of academic interest but is also an issue of debate within the United Nations. We

reach the conclusion that Global Warming is a more than well established phenomenon

occurring on our planet as result of which is an ever increasing number of weather

anomalies.

2.3 Climate Change research in other engineering fields

The issue of extreme climate change and weather phenomena has recently appeared in

publications by institutions from other engineering fields and in particular in publications of

the Institute of Structural Engineers. Cook (2003) of Anemos Associates Ltd describes how

while researching extreme wind speeds in the UK (Fig.2.4) the average trend (Fig. 2.5),

increasing at 0.12% per year, is exceeded by its standard deviation of 1.27%, Le. by 10: 1.

Moatsos, I. 2005


The standard deviation of weather stations from which data was gathered was 7.2%, or 70

times the trend, so this average trend is not likely to be significant. This does not mean

however that the observed climate changes over the last few decades have no effect on

extreme wind speeds, just that the tiny observed effect is swamped by the natural variation.

In similar research but this time in the area of climate change, Nethercot (2003) describes

how climate change will manifest itself in a greater number of extreme events and a greater

severity of the most of these. Variations will differ throughout the world, with, in some

cases, opposite effects being experienced within different parts of the UK. He also identifies

a gap in our quantitative understanding of the likely effects of climate change on the

response of structures and as a result of obvious uncertainties of the subject the tone is

deliberately one of raising issues.

2.4 Climate change current projections and implications,

The WMO and the United Nations Environment Programme jointly established the

Intergovernmental Panel on Climate change (IPCC) in 1988 to assess the scientific and

technical literature on climate change and the potential impacts of changes in climate

according to Breslin and Wang (2004). The IPCC today is looked upon as one of the pre-

eminent sources for valid assessments of the impacts of climate change. Consistent with

earlier findings, the IPCC, concluded in 2001 that the emissions of C02 resulting from the

use of fossil fuels are virtually certain to be the dominant influence on the trends in

atmospheric C02 concentration in this century. Relative to 1990, models project that

average surface temperatures will increase by 1.4°C to 5.8°C by the year 2100. In addition,

according to IPCC(2001) relative to 1990 it is projected that the global mean sea level will

rise by 0.09m to 0.88m by 2100. The IPCC also examined the implications to human

populations of temperature and sea level rise. The IPCe concluded that the human systems

that are the most sensitive to climate change include, water resources, food, forestry, coastal

zones and fisheries, human settlements, energy, industry, insurance, and human health.

Model-based projections of the mean annual number of people who may be flooded by

coastal storm surges could increase several fold, by 75 to 200 million people according to

IPCC (2001). A study commissioned in 2001 by the current Bush administration generally

agreed with the basic findings of the IPCC. The US National Research Council (2001)

concluded that:

Moatsos, I.2005


"Global warming could well have serious adverse societal and ecological

impacts by the end of this century, especially if globally-averaged

temperature increases approach the upper end of the [pee projections".

In November 2001, representatives from 160 Nations meeting in Morocco concluded

negotiations and agreed to the 1997 Kyoto Protocol. Although in attendance, the United

States was not part of the agreement, for various reasons that fall well beyond the scope of

this thesis. The treaty calls for 40 industrialized nations to reduce emissions of C02 and

other global warming gases by about 5% below 1990 levels by 2012. Fifty five nations must

ratify the treaty before it takes effect according to United Nations (2001) and the Washing

Post (2001). It appears likely that the treaty will be ratified and according to Breslin and

Wang (2004) and IPCC projections, it appears likely that the treaty as currently written is

grossly insufficient for the purpose of combating climate change in a meaningful way. If

treaties concerning ozone depleting substances, oil pollution, or the discharge of solid waste

at sea can be used as any sort of indicator, it would also appear likely that future

modifications to the Kyoto Protocol will call for ever-increasing restrictions on the

emissions and perhaps even the production of certain global warming gases.

With so much interest in global warming and its effects in the recent years, it surprising that

the marine research, design and construction communities have not started taking into

account the effects of global climate change more explicitly in their design approaches.

2.5 The Corrosion Problem

Year upon year the cost of marine corrosion has increased until it is estimated today at 4 %

of the Gross National Product for the UK according to the Marine Corrosion Forum (MCF

2005). The annual corrosion-related costs of the U.S. marine shipping industry are estimated

at $2.7 billion. This cost is divided into costs associated with new construction ($1.12

billion), with maintenance and repairs ($810 million), and with corrosion-related downtime

($785 million). Most ships that serve U.S. ports do not sail under U.S. flag, but under that of

nations with less restrictive laws and taxation; therefore, it is difficult to estimate the

national cost of corrosion for this sector. Furthermore, the shipping industry is much

diversified in terms of size, cost, and cargo. An enlightened approach to materials selection,

protection and corrosion control is needed to reduce the burden of wasted materials, wasted

Moatsos, I. 2005


energy and wasted money. The corrosive effect that sea water and cargo has on unprotected

steelwork reduces the thickness of structural members and consequently the strength of the

entire hull structure (Fig 2.6). Many different types of destructive attack can occur to

structures, ships and other equipment used in sea water service. The term 'aqueous

corrosion' describes the majority of the most troublesome problems encountered in contact

with sea water, but atmospheric corrosion of metals exposed on or near coastlines, and hot

salt corrosion in engines operating at sea or taking in salt-laden air are equally problematical

and like aqueous corrosion require a systematic approach to eliminate or manage them.

In the past corrosion allowances were "built-in" to the scantlings and the regulations for

their design in the form of a safety factors based on the class society's experience.

Structural designers in the past not receiving the correct guidance from the regulations

would also increase thicknesses to compensate for the problem leading to ships that were

significantly heavier and more expensive in their maintenance and construction designs. It

is only comparatively recently that classification societies have taken this problem into

account and rules now include a provisions for surfaces to be protected by approved coating

systems that have to be maintained in a satisfactory condition in order for the ship to remain

in class. Prior to this sacrificial anodes were often used to protect against tank corrosion but

this labour intensive method has largely been replaced (Hughes 2005).

Sea water, if not destructive enough on its own, has several powerful allies assisting the

breakdown of metals and non metals alike. Living allies in sea water also enhance its

destructive power. Microbiological organisms, cIusterings of weed, limpets as well as

deposits of sand, silt or slime not only exclude oxygen but often create locally corrosive

conditions under these deposits which aggravate attack. Coatings and composite structures

can experience rapid degradation. Sulphate reducing bacteria, left undisturbed in marine silt

or mud deposits, will produce concentrations of hydrogen sulphide which are particularly

aggressive to steel and copper based alloys.

Key factors in the prevention of marine corrosion are design, selection of materials,

construction, use and maintenance. Failings in anyone of these may lead to a total failure

to prevent attack, which once started may cost far more to correct or eliminate than any

notional savings on materials achieved at the outset. In a recent survey corrosion was found

to be responsible for 30% of failures on ships and other marine equipment according to the

Moatsos, I.2005


MeF (MeF 2005). These are expensive errors arising from the selection and use of

unsuitable materials and are compounded by ever increasing penalties on vessels, civil and

military for breakdown and unnecessarily short intervals between outages for major repairs.

On offshore platforms the cost penalty for replacement of failed equipment is several times

that required for a similar onshore facility, and this does not take into account any losses of

oil or gas production.

Corrosion remains a problem, however, as the maintenance of a protective coating can

prove to be difficult especial1y for Floating Production Storage and Offloading (FPSO)

vessels that remain in operation in a particular area for years and most servicing and repairs

have to be carried out while in operation.

2.6 Thermal stresses related failures in Ships

In the case of thermal effects on ships structures, unless the problem solved is temperature

dependent, this type of stress has often been neglected and not been taken into account in

most types of analysis. The most likely reason behind this would seem to be that the stresses

produced from temperature changes would be too small to be taken into account compared

with stil1water loads or wave bending stresses. This is not the case though. Records exist of

ships having broken in half while moored in still water and ABS in the 50s observed that

many major hull fractures occurred in still water while the temperature was changing with

the possibility that some of them might have occurred from brittle fracture at low

temperatures (Benham and Hoyle 1964). According to sse Reports (1973) records of

midship stress obtained on five bulk carriers indicated surprisingly high thermal effects.

These showed consistent diurnal variations, with magnitudes 14-24MPa (2000-3500 Psi/in)

is some cases. Very few quantitative data are available (Jasper 1956) to indicate the actual

stress and temperature variations that might be expected in a ship's voyage or even for the

duration of the vessel's life.

According to Hechtman (1956) a number of reviews on brittle fracture in ships have been

published providing the main sources of information for thermal stress investigation. Using

also a number of casualty reports describing particular failures, (Hechtman 1956)

investigated 250 casualties in which less than half provided information that permitted a

form of appraisal as to the causes of the failure in each case. In approximately 60 cases

Moatsos, I. 2005


where thermal stresses would appear significant, circumstances prevailed which would

produce thermal stresses of sufficient magnitude to be an important factor in the failure. The

larger part of the ship casualties have occurred under heavy weather. However, the term

"Heavy weather" is used to describe quite a range of intensities of wind and sea (Hechtman

1956). Some of the failures were undoubtedly the result of heavy weather alone, but most,

of the so-called heavy weather failures, would appear to entail other factors, one of which

was thermal stresses.

In a study of thermal stresses as related to ship failures, the researcher is faced with the fact

that reduced air temperature is likely to increase the temperature difference between water

and air but it also increases the tendency towards brittleness in the steel. The analysis (Fig

2.7) according to Hechtman (1956) studied these two trends covering vessels constructed

prior to 1945. No similar study has been carried out since and hence no data is available for

modem commercial vessels in any of the published literature. The upper plot, as it can be

seen in the appendix, (Fig 2.7) gives the frequency of fracture at any air temperature for

casualties of different severity. The shapes of the curves for the Group I (less severe) and

combined Group II and III casualties are similar, but the curve for the former is displaced

about 10°F lower on the temperature scale than that for the latter. When it is considered the

fairly wide range of operating temperatures in which steels in the 1950s of shell plating

thickness could exhibit brittleness, this 10°F difference does not appear to be of great

significance. It would seem that air temperature was not the only important factor in

determining the severity of the fracture. The lower plot (Fig 2.7) relates the temperature

gradient to which the ships were subjected with the frequency of casualties of different

severity. The Group II and III casualties were most frequent when the temperature gradient

was close to zero. The Group I casualties were most frequent when the air temperature was

lower than that of the water around 8 degrees Fahrenheit. This difference may seem small

until it is realised that temperature gradients of 20 degrees Fahrenheit or more are rather

infrequent in ships at sea.

The amount of unpredictable factors when in comes to ship design seems to be ever

increasing with the two of the more significant being the actual medium in which marine

vehicles are designed to operate and the weather. But questions arise as to whether we have

really managed to corne to grips with the unpredictability of the variables influencing ship

design. For thermal effects to be included in design calculations (Lewis et al. 1973), an

Moatsos, I. 2005


estimation of the magnitude of the effect under different conditions of sun exposure and an

estimation of the frequency of occurrence of these different conditions in service is required.

2.7 Approach to be followed

As already mentioned in Chapter 1 (1.3.5) during the description of the background behind

this study, the need exists for the development of more detailed approaches for the analysis

of structures that will not only accurately model the variety of extreme conditions

encountered by current and future developed marine structures, but will also not prohibit

innovative solutions and provide the basis upon which modem regulator approaches can

develop without following a strict prescriptive approach. This study aims to propose such an

approach for FPSOffanker type of marine structures by using a variety of existing

formulation and combining it in a unique way, so as to examine the best possible way to

perform such an analysis and study the effects of a variety of extreme conditions

encountered by vessels already in operation. In the next chapters of this thesis the

development of each approach and details on the formulation and analysis techniques will

be described in detail. Three vessels will be analysed, both new built vessels and

conversions, examining different structural configurations examining the effects of these

different configurations on the results to be obtained in each case.

As it is evident from the literature review, the best way of modelling thermal effects on the

structures to be analysed, needs to be examined in detail so as to enable the research to

study the effects of global warming and the corresponding extreme diurnal changes in

temperature on marine structures. This will be carried out using a modified Jasper (1956)

approach not only for the accuracy of the results that will be obtained but also due to the

fact that it has been the recommended practice by the SSC. Statistical data for a period of 20

years based on actual measurements from the North Sea will then be examined to determine

the range of temperatures to be used for analysis.

After examining published research on the accuracy of various leading ultimate strength

approaches, some of the most accurate and appropriate for the modelling of the problem,

methods will be compared to determine the best approach that will enable the resistance

component for reliability analysis to be modelled. This will be done in both component

levels (stiffened and un stiffened plate) also for the entire hull girder. All results will be

Moatsos, I. 2005


benchmarked and compared against LRPASS and industry standard software used by

Lloyds Register of Shipping and each method selected will need to have been already

benchmarked against experimental data to ensure its accuracy. Codes using Fortran and

Visual Basic will be developed building a strength model that takes into account diurnal

temperature changes and corrosion providing comparison between corrosion and ultimate

strength formulation used. The effect of corrosion models on ultimate strength results will

be examined and will also be incorporated in the codes developed. After comparing these

and selecting the best possible solution, corrosion will be applied to the strength model for a

period of 25 years without taking into account repairs and inspections, hence generating the

final resistance component to be used in reliability analysis

The loading component to be used in reliability analysis will be calculated using both

industry standard regulatory approaches and long-term statistical formulation. To examine

the effects of slamming on the hull girder and the vertical bending moment the Jensen &

Mansour (2002) approach will be used as being sophisticated enough to provide high

accuracy results without using a time and resources consuming strip theory approach but

also flexible enough to be used quickly and efficiently even at an early design stage. The

best way for combining all load components will be investigated and after comparing all

possible solutions the most appropriate formulation will be used to provide long-term

loading data, distributions and load combination factors to be used in reliability analysis.

Reliability limit state formulation will be proposed by the author after studying similar

published approaches and using a time-variant and invariant approach in combination with a

variety of reliability analysis techniques the probabilities of failure, the reliability indices

and partial safety factors (where applicable) for the vessels to be analysed shall be

calculated. Both results obtained by time-variant and invariant analyses will be compared to

examine the extent to which each approach influences the results obtained.

The combination of all aforementioned elements and the entire approach on this study is

unique, and no similar study had been found published after extensive literature review

carried out by the author and research reviews that were examined by the author that were

carried out by leading research committees and groups such as the ISSC/SSC, lACS, JCSS,

ASRANet Ship Group, The Royal Society and the Royal Academy of Engineering.

Moatsos, I. 2005


Whenever applicable the results obtained will be compared with similar data or results

available in published literature.

Concluding this study, comments will be made on the results and the approaches used but

also on the nature of the phenomena examined and what directions future research can take

in some of the fields examined. Also thoughts and issues on the results and points raised

during this investigation that require critical comments will be recorded for use by future

readers of this thesis that will enable them to use this study as the foundation for further

investigations on the examined subjects.

A detailed literature review of all components involved in this study is required as a next

step in this study and will be the subject of the next chapter, providing the foundation upon

decisions on the suitability of approaches chosen for analysis will be made.

Moatsos, I. 2005



ASRANet Networkfor Integrating Structural Analysis, Risk and Reliability Website [Online.Internet.] Available: http://www.asranet.com/. Accessed: 1 Jun, 2005.

Benham, P.P., Hoyle, R., (eds) 1964, Thermal Stress, London, Sir Isaac Pitman & Sons Ltd.

Breslin, D.A, Wang, Y-L.2004, "Climate Change, National Security, and Naval ShipDesign", Naval Engineer's Journal, Vol. 116, No.1, pp 27-40.

British-Irish Council Website, [Online. Internet.] Available:

http://www.british-irishcouncil.org/c1imatechan ge, Accessed 24 Jul 2003.

Cook, N. 2003, "Extreme Wind Speeds in the UK", The Structural Engineer, InternationalJournal ofthe Institute of Structural Engineers, Vol.81, No.8, pp 18-19.

Hadley Centre for Climate Prediction and Research, [Online. Internet.] Available:http://www.metoffice.comlresearchlhadleycentre/. Accessed 1 Jun, 2005.

Hechtman, R.A. 1956, "Thermal Stresses in Ships", Ship Structure Committee Report,Serial No. SSC-95, National Academy of Sciences-National Research Council,Washington DC, USA.

Hughes, C. 2005, "From Pig Iron to Mitten Crabs", Marine Engineer's Review, IMarEST,Dec-Jan, pp 30-31.

International Weekly Journal of Science, [Online. Internet.] Available:http://www.nature.comlnature/index.html. Accessed 22 Feb, 2004.

Jasper N.H. 1956, "Temperature-Induced Stresses in Beams and Ships", ASNE Journal,USA, Vol. 68, pp 485-497.

Intergovernmental Panel on Climate Change, 200 1a, "Summary for Policy Makers ClimateChange 2001", Working Group I Report, IPCC, USA.

Intergovernmental Panel on Climate Change, 2001b "Summary for Policy Makers ClimateChange 2001: Impacts Adaptation and Vulnerability", Working Group II Report, IPCC,USA.

International Association of Classification Societies Website [Online. Internet.] Available:http://www.iacs.org.uk/ , Accessed: 1 Jun, 2005.

Lewis, E.V., Zubaly, R.B., Hoffman, D., Maclean, W.M., Van Hoof, R. 1973, "LoadCriteria for Ship Structural Design", Ship Structure Committee Report, Serial No. SSC-240, US Coast Guard, Washington DC, USA.

Marine Corrosion Forum Website, [Online. Internet.], Available:http://www.marinecorrosionforum.org, Accessed June 6th 2005.

Nethercot, D.A. 2003, "Climate Change: the Structural Engineers' Response", TheStructural Engineer, International Journal of the Institute of Structural Engineers,Vol.81, No.1, pp 24-28.

Radford, T. 2004, "Freak Summers Will Happen Regularly", The Guardian Online [Online.Internet.] Available: http://observer.guardian.co.ukl, Guardian Newspapers Ltd,Accessed February 22nd 2004.

Ship Structure Committee Website [Online. Internet.]

Available: http://www.shipstructure.org/. Accessed: 10 Jun, 2005.

Moatsos, I. 2005

http://www.asranet.com/.

http://www.british-irishcouncil.org/c1imatechan

http://www.metoffice.comlresearchlhadleycentre/.

http://www.nature.comlnature/index.html.

http://www.iacs.org.uk/

http://www.marinecorrosionforum.org,

http://observer.guardian.co.ukl,

http://www.shipstructure.org/.


The Environment News Service Website, [Online. Internet]. Available: http://www.ens-news.com, Accessed 24 Jul, 2003.

The Joint Committee on Structural Safety Website [Online. Internet.]

Available: http://www.jcss.ethz.ch/. Accessed: 1 Jun, 2005.

Townsend, M., Harris, P. 2004, "Now the Pentagon tells Bush: Climate Change WillDestroy Us", The Observer Online, [Online. Internet.] Available:http://observer.guardian.co.ukJ, Guardian Newspapers Ltd, Accessed 22 Feb 2004.

United Nations, 2001, "Governments Ready to Ratify the Kyoto Protocol", United NationsFramework Convention on Climate change (UNFCC), Secretariat, United Nations,November 10.

US National Research Council, 2001, "Climate Change Science: An Analysis of Some KeyQuestions", National Academy Press, USA.

Washington Post, 2001, "160 Nations Agree to Warming Pact: U.S. Was on Sidelines inMorocco Talks", Washington Post, Section A, November 2001.

World Meteorological Organisation, 2002, "WMO Statement on Status of the GlobalClimate in 2002", Press Release 684, Geneva, Switzerland, 17thDecember.

World Meteorological Organisation, 2003, "Statement of Status of the Global Climate in2002", Press Release 684, Geneva, Switzerland, 17thDecember.

Moatsos, I. 2005

http://www.jcss.ethz.ch/.

http://observer.guardian.co.ukJ,


Appendix 2, Figures

0.8U 0.60.._..0 0.4enenr-I 0.2r-

<.Denr- 0E0'- -0.2-(l)uc -0.4(l)I-(l)It::CS -0.6

-0.81860

Globe

_ Temperature anomalySmoothed witha binomial filter

1880 1900 1920 1940 1960 1980 2000Figure 2.1 Combined annual land, air and sea surface temperatures (1860-2002) relative to 1961-1990.

(WM02002).

.rI*...ellll ___.1Ii"_lbIIh_~1ID!cI_ ....r.._'I!1~ 1OoIIIIoItC'

1lo::;H-

II iii: '1JII,..nSST, n~~f- tIliMtt~iJIYjf

C 10-~_.,.,..r!ctfW~ _~I"""""':------,

SignificantClimate Anomaliesand Events in 20021Io·.q gtttIlIIrlBIIlI1llt1.~ CIIt6XIIlIRAil gI:OIIllIIl=- shlt 110)_ [&'C

Figure 2.2 Global Significant Climate Anomalies in 2002 (WMO 2002).

Moatsos, 1. 2005


Figure 2.3 PRECIS Output (Hadley Centre 2005).

1200

1100

1000

900

BOO

500

400

300

200

100

o

100 200 300 400 500 600 700

Figure 2.4 Preliminary map of base wind speeds for the UK (The Structural Engineer 2003).

Moatsos, 1. 2005


11l9O

Slartyet!f

Figure 2.5 Trend in decennial extreme winds 1970-1999 for the UK (The Structural Engineer 2003).

Figure 2.6 Corrosion in Ballast Tanks (Hughes 2005).

0

I rGROUP I_

II ,Kt·I\~,J-GROUP II II litI

0I

I , \ \II '-,I

V.~ ~---\J,..............._----:- --"'w

5 0~ -20

"'.."oJ<t..o..u..o

'"'"<t...~ 2o0:

'"...

20 40 60 '0 100

AIR TEMPERATURE 1j..-F

0r,

r~I \III

0

\ L-GROUP t,

GROUP n a m"",<,,--.' ,: \~

0: I

I .' / \\. 1\

I rl \ -\I,- ~,~

... , r--~ ----0 --20 20 '0 60

-60

Figure 2.7 Air Temperature and Temperature Gradient at Time of Fracture. (Hechtman 1956).

Moatsos, I. 2005

CHAPTER3

CRITICAL REVIEW OF PUBLISHED WORK

3.1 Introduction

The complexity, academic level and level of details required for this particular study

requires the author to examine all relevant published work in corresponding fields, in order

for him to build upon his knowledge of the subject and acquire and develop the particular

tools that will enable him to provide answers to the questions that are being investigated.

During this exercise the author must determine the trustworthiness, relevance and quality of

the publications and work in each particular field of this study as a source. These will not

necessarily be published just in the marine engineering field and careful examination of

research carried out in other engineering, mathematical and science fields. This will also

enable the author of this thesis to comment upon the work of others working in similar

fields and the applicability of their findings and methodology to the subject of the particular

study. Then all the knowledge examined and critically commented can be used by the

author as a foundation upon to build this study and follow references from work on similar

fields upon which the best and most complete knowledge possible in each area can be

acquired.

3.2 Thermal Stress on ship structures published research

3.2.1 Introduction

According to Hechtman (1956) the designers of large bridges were apparently the first to

study the effect of temperature change as early as 1893 observing temperatures of 54°C in

parts of a steel arch bridge exposed to the sun and 40°C in the shaded portions when the air

temperature in the shade was 32.2°C with indications that stresses can arise from such

differential. The first published paper mentioning thermal stresses in ships dates as early as

1913 and is written by Smith (1913).

The fact that ship structures do encounter temperature conditions that induce thermal

stresses and deformation of practical importance has been recognized for some time and in

the late 50s and 60s the subject of temperature stressing in ships received particular

attention with the design and construction of vessels able to carry liquefied gases at

Moatsos, 1. 2005

Chapter 3. Critical Review of Published Work 74

temperatures down to -190°C and the carriage of liquid sulphur at temperatures in the region.of 260°C. Hechtman lists a paper by Suychiro and Inokuty (published in the 1916 volume of

the Japanese Society of Naval Architects Journal) as one of the first to be devoted

specifically to this topic. Following that papers by Hurst (1943); Corlett (1950); Jasper

(1955); Hechtman (1956) and Meriam, Lyman, Steidel and Brown (1958) have been

published and all relevant research has been well documented by the Ship Structures

Committee (SSC) which summarizes to a certain extent the pertinent investigations devoted

specifically to the effect of environmental temperatures on ship structures.

By way of comparison some 200 papers had appeared in the literature between the late

1940s and the 1960s that were written with the specific intent of contributing to the better

understanding of temperature problems associated with aircraft structures. This number

does not include some 400 additional investigations devoted to the creep behaviour of

aircraft structures and materials and a textbook on thermal stresses with applications to

aircraft and missiles written by Gatewood (1957). The 'boom' of the space race in the 1950s

and the interest of the defence industries worldwide from the 50s until today has more that

quadrupled the numbers of relevant published research since then, according to Gatewood

(1957). One might say that the environmental temperature conditions that aircraft and

missile structures vary significantly in magnitude and nature from those that ship structures

encounter. That is true. The temperature conditions encountered by supersonic aircraft and

missiles are much more severe than those encountered by ships, and for this reason it is

reasonable to expect that the aircraft structures' thermal problems would receive

considerably more attention. On the other hand, one cannot rightly say that the thermal

problems in ship structures are of so much less importance as to justify the comparatively

little attention they have received and are still receiving since the 1960s. Obviously, any

single service condition that induces stresses in the 8,000 to 12,000 psi (55-83MN/m2) range

cannot be considered negligible. That such thermal stresses can arise in ship structures from

perfectly commonplace temperature conditions has been well documented, as it can be seen

in Jasper (1955).

The problem of the stresses set up by the temperature gradients under normal operating

conditions is common to all ships the magnitude of which will be dependant on the range of

temperature changes that the structure will be submitted to. Nevertheless, the effects of

temperature for all mare structures are threefold (Gatewood 1957):

Moatsos, I. 2005


1. Temperature changes will cause a deflection of the hull

2. Temperature change can result in the properties of the material of the hull girder to

change

3. Temperature resultant stresses will be generated

3.2.2 Deflection

The early work on temperature effects in ships was concerned with the effect on the draft's

deflection of the hull. According to Bennet (1929) it can cause changes of up to 6" in draft

on a 600' Great Lake Ore Carrier. For other ships it is suggested by the same author that the

deflection due to temperature variations normally encountered in service is small and of

secondary importance to the stresses.

3.2.3 Changes in Properties ofMaterial

Hechtman (1957) studied a number of failures resulting from brittle fractures brought about

by low temperatures and the increased tensile stresses consequent upon sudden changes in

temperature. There is little information on the changes in the other properties of steel in the

range of temperatures above OnCwhich are likely to be encountered. A survey of available

literature is given by Meikle and Binning (1961) according to Miller (1961) which includes

some data of tests conducted. Mounce, Crossett and Armstrong (1959) reported on the

properties of steel suitable for the containment of liquid gases down to -270°C. The

particular paper also discusses the brittle fracture problem under such conditions. It is made

clear in the discussion part of this paper that carbon steels now exist that have satisfactory

brittle fracture properties down to -40°C, which cover the extremes of cold temperatures

experienced by ordinary vessels.

As a result of the aeronautics industry interest, data on the behaviour of aluminium alloys

under high temperature conditions are more commonly available and have been recorded by

Hoyt (1952) for a variety of metals and a number of stressing problems involving

aluminium at elevated temperatures have been discussed by Gatewood (1960). In low

temperatures considerable research has been carried out on the use of aluminium alloys for

the storage of liquefied gases as reported by Mounce, Crossett and Armstrong (1959) and

comparisons show that for liquefied gas container vessels, both steel and aluminium alloys

Moatsos, I. 2005


are today commonly available, which have satisfactory properties that include resistance to

brittle fracture.

3.2.4 Temperature Stresses

The most extensive study of temperature induced stresses so far has been undoubtedly

carried out by Hechtman (1956) in which the conditions that existed at the time of failure of

a large number of ships has been examined, reaching the conclusion that temperature

stresses would have been present to a considerable degree in about 50% of the cases

examined. Zubaly, as it can be seen in Lewis et al. (1973), suggested that a programme of

research should be instituted to determine the maximum variations in temperature likely to

occur on anyone sea route but the numbers of factors affecting any particular ship are so

large that to obtain reliable results a very large number of ships would have to be

instrumented. Hence research concentrates in the determination of extreme gradients that

may occur and estimating the stresses which will arise in particular cases.

3.2.5 Calculation of Temperature Gradients and Thermal Stresses>

Theoretical and Experimental

There is considerable literature on heat transfer with McAdams (1960) providing a good

bibliography on the subject, but with ship structures, loading and operating conditions being

so complicated, not much of this work is directly applicable. Full scale tests as reported by

Meriam et al. (1958) and Ossowski (1960) have provided relatively accurate results for

temperature gradients which will arise away from structural details only for liquefied cargo

ships.

The calculation of the longitudinal stresses in the hull girder resulting from two dimensional

temperature gradients has been the subject of several papers written by Hurst (1943), Corlett

(1950) and Jasper (1955). All the methods and procedure suggested produce relatively

similar results and it is considered that Jasper's statement of the problem, based on

Timoshenko's Theory, is the clearest and easiest to apply showing good agreement with

experimental values on both the model and full scale tests as reported by Meriam et

a1.(1958), Ossowski (1960) and Corlett (1950).

Moatsos, I. 2005


Hechtman (1956) also gives a short list of temperature-stress problems that have been

solved and the bibliography in Gatewood (1957) gives a very extensive list of references.

Unfortunately nearly all of the references are connected with aircraft problems and very few

of the solutions can be applied directly to ships but they do supply much valuable

information on theoretical and experimental techniques which can be applied to ships

related problems.

The earliest data on temperature stresses were produced as a by-product of full scale test on

ships to determine the behaviour of the hull girder under various loading conditions. A

review of the data obtained from the early tests is given by Hechtman (1956) and Corlett

(1950) carried out tests on a box shaped model made of steel with an aluminium

superstructure under controlled temperature conditions with good confirmation of the two

dimensional theory. In the 1960s a very extensive investigation has been carried out on

behalf of the S.10 Panel of SNAME as reported by Meriam et al. (1958). As also reported

by the SSC (Kaplan, Benatar, Bentson & Achtarides 1984) records exist of full scale

measurements on 2 vessels (S.S. Wolverine State & ESSO Malaysia) giving information on

the statistical nature of the thermal stresses experienced by these vessel during their voyages

and pointing out the significance in the magnitude of the thermal stresses encountered.

Of significance, since very little thermal stress research has been published since the late

1960s, is the published work of Shi, Thompson & Le Hire (1996) analysing temperature and

hull stress signals recorded from a container ship (double skinned) and a bulk carrier (single

skinned) (Fig. l-Fig. 5) examining stress variations in response to representative changes in

these vessels using both beam bending and finite element approaches (Fig. 6). In addition to

this using similar approaches to the pioneering work on thermal stresses published in the

1950s, work on thermal stresses has been recently published by Du (1991) reviewing and

comparing existing methodology and by Heder, Josefson & Ulvfarson (1991) calculating

the thermal deformations and stresses in OBO vessels carrying heated cargo. Some of the

most significant publications and work on thermal stress can be found in a summarised form

in the Appendix (Table 3.1).

Moatsos, I.2005


3.3 Ultimate strength of ship structures published research

3.3.1 Introduction

The longitudinal strength of a vessel, as is otherwise known the ability of a ship to

withstand longitudinal bending under operational and extreme loads without suffering

failure, is one of the most fundamental aspects of the strength of a ship and of primary

importance for Naval Architects. Assessment of the ability of the ship hull girder to carry

such loads involves the evaluation of the capacity of the hull girder under longitudinal

bending and also the estimation of the maximum bending moment which may act on it.

From the initial work of pioneers in the area of ship structural design such as the likes of

Thomas Young and Sir Isambard K. BruneI and Timoshenko the fundamental idea to assess

longitudinal strength of a ship's hull was first presented by John (1874). By calculating the

bending moment assuming the wave whose length is equal to the ship length he proposed an

approximate formula to evaluate the bending moment at a midship section. He also

calculated the deck maximum stress and by comparing that to the material breaking strength

he managed to determine the panel optimum thickness. Although John's theory remains in

use until today, subsequent methods of stress analysis and wave loading have improved

substantially with criteria that help to determine optimal thickness changing from breaking

strength to yield strength. One of the most recent developments in that area is that of taking

into account, when assessing the hull girder strength, the ultimate strength of the hull girder.

Stiffened plates are the most common and versatile structural units used today worldwide in

a variety of structural applications ranging from buildings and bridges to ships, offshore and

sub-sea structures and aeroplanes. Although research on the behaviour and strength of

stiffened plates dates back to the last century, a large number of notable theoretical studies

have been carried out since the 1970s. Post-buckling behaviour of plates loaded in

compression has been studied in great detail by various sources and many design methods

employing empirical solutions are widely available in the published literature. An excellent

review on pre-1975 available unstiffened plating formulation can be found in Faulkner

(1975) and for stiffened plating in Guedes Soares & Soreide (1983).

Moatsos, I. 2005


3.3.2 Stiffened and Unstiffened Plate Ultimate Strength

Since the 1970s, when the pioneering work by Smith (1975) was perhaps the most

significant work in the ultimate strength structural design area, several new methods have

been published for plates examining their post-buckling behaviour when loaded in

compression with Vilnay & Rockley (1981) proposing a generalised effective width formula

which was based on the numerical results by Frieze et al. (1976), Smith, Davidson,

Chapman & Dowling (1987) investigated the strength and stiffness of stiffened plating

under in-plane compression and tension for imperfect rectangular plates through a

combination of nonlinear PEA and regression analysis of test results, Chen et al. (1983)

investigated buckling and post-buckling strength of individual structural components using

an PEA approach and Rhodes (1981) proposing a simple method to generate the load-

shortening curve of plates loaded in compression which although shows good agreement

with some numerical methods for perfect plate, the results for imperfect plates, especially in

the cases of initial deflection over 30% of plate thickness not being very satisfactory. Using

a similar approach Bonello, Chryssanthopoulos & Dowling (1991) presented strength

formulation for unstiffened plates in which two characteristic points in load-shortening

curves were defined. Unfortunately since two parameters in the procedure are still obtained

from two groups of curves derived from numerical load-shortening curves, the method

seems to be not very suitable for design purposes. Both the Bonello et al. (1991) and the

Rhodes (1981) approaches have as their main philosophy to establish post buckling curves

which again makes them unsuitable for design purposes. On the other hand Guedes Soares

(1988a) developed formulation in which the initial deflection and residual stress could be

explicitly considered based on existing experimental and numerical data which shows very

good agreement when compared with other analytical and experimental results and

Davidson, Chapman, Smith, & Dowling (1991) also derived empirical formulation for

plating.

For stiffened plating work has been published by Carlsen (1980), based on the Perry-

Robertson formula, adopting the criteria for initial yielding in the outer fibres. Also based

on the Perry-Robertson formulae Bonello, Chryssanthopoulos & Dowling (1992) proposed

a formulation in which both compression and lateral pressure are considered. According to

Guedes Soares (1983) when comparing available formulation in the 1980s the approach

Moatsos, I. 2005


suggested by Faulkner (1975) provided better behaviour prediction and this approach was

extended by Pu & Das (1994) to incorporate more recent research results in plate panels.

Since then work has been published by Paik & Pedersen (1995, 1996) on simplified

methods for predicting the ultimate strength of stiffened panels with initial deflections based

on large deflection theory, rigid-plastic analysis based on the collapse mechanism taking

into account large deformation effects. Approximate methods have also been suggested by

Gordo & Guedes Soares (1996) which have been compared with all the available and

published tests on stiffened plates and FE code results showing good correlation.

A significant volume of work has been published by Paik, with various other co-authors, on

analytical methods for calculating the ultimate compressive strength of stiffened panels,

first appearing in Paik & Kim (1997) and also published in Paik, Thayamballi & Kim

(1999), which has been improved and extended to include combined axial loads, edge shear

and lateral pressure in Paik, Thayamballi & Kim (2000) and Paik, Thayamballi, Kim,

Wang, Shin & Liu (2000), incorporated in the ALPSIULSAP Computer Program (Paik,

Lee, Kim, Lee, Hughes & Riga, 2000) and can be found in their latest form in Paik,

Thayamballi & Kim (200 1)

More recently Mansour & Masaoka (2004) have proposed new simple design equations

modelling the ultimate compressive strength of imperfect unstiffened plates; Assakkaf &

Ayyub (2004) compared various bias and uncertainty approaches for load and resistance

factor design (LRFD) rues for stiffened gross panels of ship structures; Egorov &

Kozlyakov (2004) analysed ultimate loads on ship grillages accounting for the simultaneous

action of ultimate bending moments at total longitudinal bending and pressures on the

grillages, taking into account plastic bending, shear & torsion; Steen, Byklum, Vliming &

0stvold (2004) have applied geometrical non-linear plate theory forming part of the Det

Norske Veritas (DNV) Panel Ultimate Limit State (PULS) code which forms part of the

new DNV rules and standards for ships and offshore structures, validating their code against

non-lnear FE analyses, existing Class Society codes and laboratory experiments and

. Keding, Olaru & Fujikubo (2004) developed ISUM plate elements considering lateral

pressure effects and compared them with FE analysis demonstrating the applicability of the

approach to stiffened plates. Some of the most significant publications and work on

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Chapter 3. Critical Review ofPuhlished Work 81

stiffened and unstiffened ultimate strength research can be found in a summarised form in

the Appendix (Table 3.2), (Table 3.3).

3.3.3 Hull Girder Ultimate Strength

With two methods being more dominant over others that are used to evaluate the ultimate

hull girder strength of a vessel under longitudinal bending a number of different opinions

exist on which leads to more accurate results. One calculates the ultimate hull girder

strength directly and the other performs a progressive collapse analysis on a hull girder.

Work by Caldwell (1965) originally attempted theoretically to evaluate the ultimate hull

girder strength of a vessel. He introduced "Plastic Design", as it is known today, by

considering the influence of buckling and yielding of structural members composing a

ship's hull. By introducing a stress reduction factor at the compression side of bending he

managed to calculate the bending moment produced by the reduced stress which he

considered as the ultimate hull girder strength. By not taking into account the reduction in

the capacity of structural members beyond their ultimate strength his method overestimates

the hull girder's ultimate strength in general and since exact values of reduction factors for

structural members were not known, the "real" value could not be calculated, only an

approximation. Since then it has been improved by work carried out by Maestro and Marino

(1989) and Nishihara (1983) who extended the formulation to include bi-axial bending,

modified it to such extent as to be able to estimate the influence of damage due to grounding

and to improve the accuracy of the strength reduction factor. By proposing their own

formulae Edo et al. (1988) and Mansour et a1. (1990) performed simple calculations that

lead to the development of further methods like the one proposed by Paik and Mansour

(1995). By applying this Paik et a1. (1997) performed reliability analysis considering

corrosion damage. Although these methods do not explicitly take into account of the

strength reduction in the members, the evaluated ultimate strength showed good correlation

with measured/calculated results from other cases. Paik and Mansour (1995) compared the

predicted results with those by experiments and Idealized Structural Unit Method (ISUM)

analysis and the differences between the two were found to be between -1.9% and +9.1 %.

By taking into account the strength reduction (load shedding) of structural members when

the collapse behaviour of a ship's hull is simulated, a number of methods were developed

which can be grouped under the overall term "Progressive Collapse Analysis" whose

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fundamental part could be the application of the Finite Element Method (FEM) considering

both geometrical and material nonlinearities. Unfortunately the large amount of computer

resources required to perform such type of analysis and to reassure the reliability of the

subsequent results has lead to the development of simplified methods such as the one

proposed by Smith (1977). This is done by taking into account the strength reduction of

structural members after their ultimate strength as well as the time lag in collapse of

individual members and Smith was also the first to demonstrate that the cross-section

cannot sustain fully plastic bending moment. The accuracy of the derived results depends

largely on the accuracy of the average stress strain relationships of the elements. Problems

in the use of the method occur from modelling of initial imperfections (deflection and

welding residual stresses) and the boundary conditions (multi-span model, interaction

between adjacent elements). To improve this recent research is focusing on the development

of more reliable stress-strain curves and it can be seen in work by Gordo & Guedes Soares

(1993) and Paik (1999). Smith also performed a series of elasto-plastic large deflection

analysis by FEM to derive the average stress-strain relationships of elements and analytical

methods have been proposed such as the one by Ostapenko (1981) which includes

combined applied in-plane bending and shear as well as combined thrust and hydraulic

pressure. Rutherford and Caldwell (1990) proposed an analytical method combining the

ultimate strength formulae and solution of the rigid-plastic mechanism analysis. In both

methods, the strength reduction after the ultimate strength is considered. Yao (1993) also

proposed an analytical method to derive average stress-strain relationship for the element

composed of a stiffener and attached plating which derives average stress-strain

relationships for the panel by combining the elastic large deflection analysis and the rigid-

plastic mechanism analysis in analytical forms from work performed by Yao and Nikolov

(1991) & (1992). Then by taking into account the equilibrium condition of forces and

bending moments acting on the element the relationships are derived. When the stiffener

part is elastic, a sinusoidal deflection mode is assumed, whereas after the yielding has

started, a plastic deflection component is introduced which gives constant curvature at the

yielded mid-span region. A number of practical applications of the methods mentioned here

have been published with one of the most significant being the investigation of the causes of

the loss of the Energy Conservation VLCC by Rutherford and Caldwell (1990) by

performing progressive collapse analysis.

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With simplified methods for progressive collapse analysis, the applications of ordinary

FEM are very few due to the influences of both material and geometrical nonlinearities

which have to be considered when applying such an incremental procedure. With a ship's

hull girder being, perhaps, too large for such kind of analysis to get rational results easily, a

number of some significant works has, nevertheless, been published. Chen et al. (1983) and

Kutt et al. (1985) performed static and dynamic FEM analyses modelling a part of a ship

hull with plate and beam-column elements and orthotropic plate elements representing

stiffened plate and discussed the sensitivities of the ultimate hull girder strength with

respect to yield stress, plate thickness and initial imperfection based on the calculated

results. Valsgaard et al. (1991) analysed the progressive collapse behaviour of the girder

models tested by Mansour et al. (1990) and Energy concentration but unfortunately there

are not many results of FEM analysis evaluation of ultimate hull girder strength are not so

many at the moment because the number of elements and nodal points become very huge if

rational results are required.

Apart from Smith's method, the Idealized Structural Unit Method (ISUM) is another simple

procedure that takes into account a larger structural unit considered as one element thus

reducing the computational time required to achieve results. The essential point of this

method is to develop effective and simple element (dynamical model) considering the

influences of both buckling and yielding. Ueda et al. (1984) developed plate and stiffened

plate elements that accurately simulate buckling/plastic collapse behaviour under combined

bi-axial compression/tension and shear loads. Paik improved this work and performed

different progressive collapse analyses as published in Paik et al. (1990) and (1992). Ueda

and Rashed (1991) improved their results with Paik (1994) following with an attempt to

introduce the influence of tensile behaviour of elements in ISUM. Finally Bai et al. (1993)

developed beam element, plate element and shear element based on the Plastic Node

Method, as originally published by Ueda and Yao (1982) and managed to achieve

progressive collapse analysis. While in Smith's method accurate results are obtained when

only the bending moment is acting, the ISUM can be applicable for the case with any

combination of compression/tension, bending, shear and torsion loadings but sophisticated

elements are required to get accurate results and to improve this ISUM elements are still

under development.

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Using modified Smith (1975) approaches, Gordo, Guedes Soares & Faulkner (1996) and

Rahman & Chowdhury (1996) have looked into simplified approaches for the determination

of the ultimate longitudinal strength of the hull girder of ships. Paik (2004b) has suggested

principles and criteria for ultimate limit state design and strength assessment of ship hulls

based on work that he has previously published and Yao et al. (2004) have investigated the

influence of warping due to vertical shear force on the ultimate hull girder strength. Some of

the most significant publications and work on ultimate hull girder strength research can be

found in a summarised form in the Appendix (Table 3.4).

3.4 Corrosion effects on ship structures published research

3.4.1 Introduction

According to Paik (2004c), corrosion appears as non-protective, friable rust, largely on

internal surfaces that are unprotected. Over time, the rust scale continually breaks off,

exposing fresh metal to corrosive attack. Thickness loss cannot sometimes be judged

visually until excessive loss has occurred. Failure to remove mill scale during construction

of the ship can accelerate the corrosion experienced in service and severe corrosion, usually

characterized by heavy scale accumulation, can lead to significant steel renewals. It is

important to realize that the corrosion process of seawater ballast tank structures can be

different from that of "at-sea" stationary immersion corrosion. Water temperature inside

ballast tanks is normally warmer than that at sea condition. In loading and unloading

cargoes at harbour, ballasting and de-ballasting will also occur in order to adjust freeboard

or trim. Such ballast cycles may accelerate the corrosion process as a result of the steel

surface becoming repeatedly dry or wet by seawater. Where coatings are present, the

progress of corrosion will normally very much depend on the degradation of such anti-

corrosion coatings. Structural flexing due to wave loading could also increase corrosion

rates due to the continuing loss of scale and exposure of new surface to corrosion. While

most classification societies usually recommend carrying out of maintenance for the

corrosion protection system in time, this may not always be the case in reality unless safety

is likely to be compromised. Extensive studies related to corrosion of ship structures have

previously been undertaken in the literature, addressing the fundamental of the corrosion

mechanism and the related factors affecting the progress of corrosion, and useful

mathematical models have been developed to predict the time-variant corrosion wastage of

ship structures.

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3.4.2 Corrosion Modelling

The conventional models of corrosion assume a constant corrosion rate, leading to a linear

relationship between the material lost and time. Southwell et al. (1979) proposed both a

linear and bi-linear corrosion model for design purposes, Melchers and Ahammed (1998)

have suggested both a steady-state model and a power approximation and Yamamoto&

Ikegami (1998) presented results of analysis of corrosion wastage in different location of

many ships, exhibiting the non-linear time dependence of time and a tendency of levelling-

off. Guedes Soares (Guedes Soares (1988b), Guedes Soares and Garbatov (1996), Guedes

Soares and Garbatov (1998) have studied the time-dependant reliability of ships hulls in

which plates are subjected to corrosion and repair actions and the reliability of plate

elements under compressive forces using initially constant corrosion rates independent of

time and in Guedes Soares and Garbatov (1999) using a non-linear general corrosion

wastage model.

An attempt to establish realistic corrosion rates for ship plates as a function of different

environmental conditions has been considered by a number of authors for different areas of

the ship hull as proposed by Akita (1983), for different types of ships as suggested by the

Tanker Structure Cooperative Forum (1992), depending on the ocean area and steel type as

suggested by Boy and Fink (1979) and Maximadj et al. (1982) and as an input for optimal

inspection strategies as suggested by Ma et al.(1997) and Huang et a1.(1997).The problem

of change in compressive strength due to corrosion has also attracted the interest of several

researchers, most notably of Hart et al. (1986) White and Ayyub (1992) and Shi (1993).

More recently Paik et al. (2003) have proposed a time-dependent corrosion wastage model

for single and double hulled tankers that can also be used for FSOs and FPSOs and Qin &

Cui (2003) have also proposed an alternative corrosion model which takes into account the

corrosion protection system's life (CPS) and the interaction between the CPS and the

environment and the accelerating and decelerating phases of corrosion once the CPS breaks

down. Melchers (2003a, 2003b) has proposed a probabilistic model for "at sea" immersion

corrosion of mild and low alloy steels based on fundamental physiochemical corrosion

mechanics and in MeIchers (2003b) has examined the process of pitting corrosion of mild

steel in a marine immersion environment. Some of the most significant publications and

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work on corrosion of marine structures can be found in a summarised form in the Appendix

(Table 3.5).

3.5 Still Water Loads critical review of work.

The issue of statistical analysis of still water bending moment (SWBM) has been addressed

since the 1970' s and quite a significant volume of published work exists on the subject. The

idea that any ship has probability distributions of SWBM was first supported by Lewis et al.

(1973) based on limited data of several cargo ships and one bulk carrier. Ivanov and

Madjarov (1975) fitted the normalized maximum SWBM by a normal distribution

according to full or partial cargo load conditions from eight cargo ships for periods of two

to seven years. Mano et al. (1977) studied the nature of still water conditions by surveying

log-books of 10 container ships and 13 tankers, and concluded that their distribution is

approximately normal, as shown in (Fig.3.7). Dalzell et al. (1979) examined the service and

full scale stress data of a large, fast containership, a VLCC, and a bulk carrier. They

concluded that the still water bending stress variations appear to be random and subject to

. the control of their extremes by the operators.

In the early 1980's some still water bending stresses of different ships were reported by

Akita (1982) as a result of work carried out in Japan. This information was presented

separately for a group of 10 containerships as well as for a group of 8 tankers. Based on

this, Kaplan et al. (1984) found that the coefficient of variation (COV) of SWBM for

containerships is 0.29 and for tankers it is 0.99 for ballast condition and 0.52 for full load

condition. More recently, Soares and Moan (1988) analyzed SWBM resulting from about

2000 voyages for 100 ships belonging to 39 ship-owners in 14 countries. Still water load

effects were assumed to vary from voyage to voyage for a particular ship, from one ship to

another in a particular class of hips and also from one class of ships to another. The analysis

was centred on the mean values and standard deviations of the loads in the critical midship

region. The still water loads were treated as ordinary random variables and in the results the

authors reported a very large variability for tankers.

3.6 Wave-Induced Loads

The most important load parameter in the structural design of ships is undoubtedly the

wave-induced vertical bending moment. Vast numbers of published research work on

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calculating wave induced loads using a variety of approaches ranging from simplified

formulas to Computational Fluid Dynamics (CFD) approaches exist. The most common

way to establish design loads by direct calculations is by the means of a long-term

description of the response. This requires that a wide range of sea states and operational

conditions must be analyzed and that the final distribution is obtained as a weighted sum of

these stationary conditions. In addition, information about routes and operational profiles

must be obtained. If linear response analyses are conducted, the response in a given

stationary condition is defined by the transfer function, while time domain simulations are

in general required to obtain the nonlinear response. This can lead to a very time and

resources consuming analysis. Simplified methods are necessary to improve the efficiency

of the direct calculation of the nonlinear long-term extreme values. Any attempt to

investigate all possible approaches would fall well beyond the scope of this study. Focusing

our attention to simplified procedures and closed form approaches, that have been compared

with other available methods and validated against experimental and full scale measurement

data; these can easily be used to provide a good estimate of mean values for use in

reliability based structural analysis.

Pioneering work by Ochi (1981) and Mansour (1981) on the principles of extreme value

statistics, their combination for reliability-based designs and their application to ships, set

the way for simplified methods such as the work of Guedes Soares (1984), Farnes (1990),

Farnes & Moan (1994), Videiro (1998) and Videiro & Moan (1999) in the application of a

direct long-term approach to non-Gaussian response. This may be executed in a variety of

ways, such as using design waves and design sea states.

Discussion of the present state of the art in wave induced load calculation methodology can

be found in ISSC 2000 Committee VI.I (2000) reports. Several ingenious procedures have

been developed in order to reduce the computational effort either by proper selection of the

most important sea states, such as the ones suggested by Adegeest et al. (1998) and Sagli

Baarholm & Moan (2001), or to simplify the non-linear analysis to second or higher order

Volterra equations, such as the ones suggested by Jensen, Petersen and Pedersen (1990) and

Pastor (2001). Generally such direct calculation procedures are not very useful at the

conceptual design phase because of the lack of detailed data for the ship analysed and

because it requires significant expertise and time to perform the calculations.

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Notable work has been published by Ferro & Mansour (1985) on the probabilistic analysis

of combined slamming and wave-induced responses but also by Friis Hansen (1994) on the

combination of slamming and wave induced responses for ships. Significant work on the

magnitude of the bow flare slamming loads of wedge-shaped sections has been published by

Zhao & FIatinsen (1993) and for green water loads by Buchner (1995) and Wang et al.

(1998). The phase lag relative to the wave-induced peak and the decay rate are mainly

derived from experimental results such as the work of Sikora (1998). Mansour & Wasson

(1995) published a methodology for developing charts for preliminary estimates of the

nonlinearities associated with wave bending moments acting on ships moving on stationary

seas. More recently Sagli Barholm & Jensen (2004) have investigated the influence of

whipping on long-term extreme vertical bending moment by considering only a few short-

term sea states that have a certain probability of occurrence, known as the contour line

approach.

3.7 Load combination

It is not an easy task to combine all the relevant extreme loads at the same time and hence

we have to focus our interest in the most important combination problem, the combination

of SWBM and VWBM in the long term, i.e., in a ship's design lifetime. For this to be

achieved it would be interesting to also examine, as it has been discussed previously in all

relevant elements of this thesis, the volume of published work on the subject. In the existing

ship rules, such as DNV (2005) and lACS Requirements S 11 (2003) and S7 (1989) these

two loads are simply added together following the peak coincidence method which assumes

that the maximum values of the two loads occur at the same instant during a ship's design

lifetime. In addition lACS also specifies that the maximum SWBM and VWBM should not

exceed their respective allowable values, even if one of the moments is negligible, based on

Nitta (1994).

Soding (1979) combined SWBM and VWBM by modelling them as random variables.

Although this approach is more rational than the peak coincidence method, it is simplistic to

model SWBM and VWBM as random variables rather than physically correct random

processes. Besides, Soding's solution was conditioned upon the assumption that the SWBM

is a normal variable and the VWBM is an exponential variable. Moan and Jiao (1988)

considered both SWBM and VWBM as stochastic processes, and, based on a particular

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solution by Larrabee (1978) they introduced a load combination factor to reduce the

conservatism inherent in the peak coincidence method as adopted by the existing ship rules.

While this approach has been the most rational, the accuracy in applying Larrabee's

solution remains to be verified against other acceptable load combination methods.

Furthermore Moan and Jiao (1988) considered the sagging condition only. Extension is then

needed with regard to the hogging condition.

Mansour & Jensen (1995) have published work on simplified approaches for the

preliminary estimate of characteristic extreme values of combined slightly non-linear loads

on ships and Guedes Soares (1995) has published work on modelling the directionality of

waves in the calculation of long-term wave-induced load effects on ships.

3.8 Reliability Based Structural Analysis.

3.8.1 IntroductionHaving examined all research work individually contributing to the aims of this study, it is

of paramount importance to also examine and comment on the work that combines all these

elements in similar approaches to the one used by the author, in an attempt to compare the

advantages and disadvantages of each method. Although all attempts to combine all the

individual methodology into a unified approach can be very dissimilar to each other, one

does not fail to recognise similar elements in the effort to mathematically model the

physical phenomena and their random nature.

3.8.2 Reliability Analysis

Reliability theory of engineering structural systems has three significant parts:

• Identification of all possible dominant failure modes.

• Calculation of the failure probability and sensitivity with respect to the obtained

dominant limit states.

• Determination of the upper and lower bounds of the overall structural system

according to the correlation between the dominant failure modes and their failure

probability.

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The identification of the dominant failure mode is performed by either traditional mechanics

or a mathematical programming approach. Although all proposed methods in this field show

a significant amount of effectiveness, the computational effort is still quite demanding for

complex structural systems. No close form of the limit states can be obtained since

numerical methods calculate the response. As an alternative, work has also focused on the

analysis of structural components or the local behaviour of a structural system.

The determination of the failure probability is the most researched part of all parts

comprising the theory of reliability. Work by Cornell (1969), Hasofer and Lind (1974) and

Shinozhuka et al. (1983) has produced the First Order and Second Order Moment theories

(FOSM and SOSM) which are well established and have found an ever-increasing use in a

significant amount of engineering fields. In this type of theory the integration of the joint

probability density function of the design variables is circumvented by transformation of the

actual problem into a least distance problem in standard normal space. Orthogonal

transform is used to uncouple the correlated design variables which essential shows that the

problem is in its core an optimization procedure.

A number of insurmountable problems in numerical integration of highly dimensional Joint

Probability Density Functions (JPDFs) in normal space lead research into the conclusion

that the failure probability of the structural system has not be given in a "weak form".

Instead of calculating the failure probability itself, an interval is given to bond the exact

value. Two methods have been proposed to help achieve this, the Wide Bound Method as

proposed by Cornell (1967) and the Narrow Bound Method as proposed by Ditlevsen

(1979). They are first order and second order approximations respectively. However with

the increase of failure modes and their correlation, the bounds will become too loose. In this

case, formulation of higher order approximations can be developed or different point

evaluation techniques can be used such as the ones proposed by Ang et al. (1981) and Song

(1992). A modified bound method can also be found in Cornell's (1967) original work.

Monte Carlo Simulation (MSC) also plays a very important role in different levels of

reliability analysis. The high accuracy that the method produces is only dependent on the

sampling number and is not affected by the distribution type and the number of basic

variables. The method can be used in even those cases where the limit state function is not

known implicitly and it is the only approach to highly non-linear problems. A number of

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variation reduction techniques have been proposed such as the Importance Sampling

Method but as always the computation cost in large complex structural systems is still

significantly high.

The Response Surface Method (RSM) is one of the latest developments in the field of

structural reliability analysis. It is very suitable in cases where the limit state function is

known only point-wisely by such numerical methods as the FEM rather than in closed form.

In essence, RSM is a system identification procedure, in which a transfer function relates

the input parameters (loading and system conditions) to the output (response in terms of

displacements or stresses). The observations required for the identification of the most

suitable way to relate those two are usually taken from systematic numerical experiments

with the full mechanical model and the transfer function obtained approximately defined as

the response surface (RS). The basis of the RSM can be tracked back to the 50s in the

experimental field, but only recently, it has been introduced into the field of reliability

analysis. It combines deterministic structural analysis software and the basic reliability ideas

aforementioned. In addition to this, even for those problems that other approximate methods

seem to be susceptible to, the RSM is shown to be superior in both accuracy and efficiency

with its only drawbacks being the experiment design and the identification of unknown

parameters in the RS which influence the whole algorithm. Work by Bucher (1990) and

Rajashekhar (1993) lead the ways for future research. Advanced algorithms based on that

work can be found in work published by Kim et al. (1997), Zheng & Das (2000) and Yu,

Das & Zheng (2001).

More recently Lua & Hess (2003) have proposed a hybrid reliability methodology for

predicting the safety of single and advanced double-hull ship structures. Some of the most

significant publications and work on structural reliability analysis research can be found in a

summarised form in the Appendix (Table 3.6).

3.9 Combinatorial Published WorkThe idea of implementing reliability methods to marine structures goes back to the early

1980s (Mansour. Jan. Zigelman, Chen & Harding. 1984) when for the first time frameworks

of procedures that can be applied to ship structures were published. As part of a project

entitled "Probability Based Ship Design Procedures-a Demonstration" undertaken by the

Ship Structure Committee (SSC) in the thrust area of reliability-based ship design. for the

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first time, in full, a framework was demonstrated of how probability based safety analysis

can be implemented in detail in ship structural analysis (Mansour, Lin, Hovem &

Thayamballi, 1993, Mansour & Hovem 1994). Since then a significant amount of work that

combines reliability based procedures with ultimate strength of ship structures and corrosion

has been published by various authors but most notably, Wang, Jiao & Moan (1996) on

structural reliability of stiffened panels on FPSOs considering load combination and

ultimate strength using a FEA approach, Paik , Kim, Yang & Thayamballi (1997) on the

ultimate strength reliability of corroded tanker hulls using closed form formulation for the

determination of the ultimate strength and a corrosion model based on actual measurements

from tankers. Wirsching, Ferensic & Thayamballi (1997) looked at the reliability of

corroding ship hulls and the effect on the ultimate strength as a function of the section

modulus using a linear corrosion wastage model and Guedes Soares & Garbatov (1999)

investigated the reliability of maintained ship hull subjected to corrosion and fatigue under

combined loading, using mathematical corrosion models suggested by the same authors.

Paik et al. (1998) using ultimate strength and corrosion formulation that he has suggested in

previous work has also investigated the same issues. Also notable is the work of Guedes

Soares & Texeira (2000) on the structural reliability of bulk carriers using long term loading

formulation and analytical formulation for the determination of the ultimate strength and

which also has a sensitivity study on the effects of the variables in the different loading

conditions and the time variant probability of failure. Looking at time dependent reliability

assessment of corroding ship hull structures notable work has been published by Sun & Bai

(2000) and Akpan, Koko, Ayyub & Dunbar (2002, 2003), modelled corrosion as a time

dependent random function and used SORM to calculate the instantaneous reliability of the

primary hull structure. Using a similar approach but investigating the effects of fatigue

cracks on the tensile and compressive residual ultimate strength of stiffened panels and

unstiffened plates using FEA Hu & Cui (2004) applied their recommended procedure to a

tanker structure taking into account the effects of inspection and repair. Furthermore Sun &

Bai (2003) also examined the time variant reliability of specifically FPSO structures, with

emphasis on crack propagation and corrosion, using an analytical approach for the

determination of the ultimate strength and the Ferry-Borges method for the combination of

stochastic loading. A very informative review of the latest developments regarding safety

management of floating structures can be found in Moan (2004).

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Paik (2004a) published a practical guide for ultimate longitudinal strength assessment of

ships comparing progressive collapse analysis & closed form design formulas which will

form the core of the ISO code 18072-2: ships and Marine Technology-Ship Structures-Part

2: Requirements of their Ultimate Strength Assessment. Significant work in the field has

also been published by Guedes Soares et al. (1996) providing calibration of partial safety

factors (PSF) for ship structural design through improved models of linear and non-linear

load effects using long term formulation. Through reliability assessment of several tankers

and containerships as part of the SHIPREL project the basis was set for the definition of a

target safety level which was used to assess the partial safety factors suitable for use in a

new design rule format to be adopted in modern ship structural design. Some of the most

significant publications and work on combining all the aforementioned research for use in

structural reliability analysis and design of marine structures can be found in a summarised

form in the Appendix (Table 3.7).

3.10 Discussion-RemarksWhile a number of useful methodologies for analysing the safety and reliability of ship

structures have been developed over the past decades, as discussed in all the previous

sections of this Chapter, further developments are needed. Some further considerations in

probability-based design of ship structures are as follows:

• Geometric parameters may be treated as deterministic, although this may need to be

confirmed in the case of deck and bottom plating thickness.

• Elastic modulus may be taken as deterministic, but yield stress needs to be treated as

a random variable with a mean value based on a fuller assessment of strain-rate

effects on yield in large scale representative ship-type structures. In the first

instance, yield stress values could be based on tensile coupon test results when

wave-induced bending moments dominate, and similarly derived static values of

yield stress for dominant still water load conditions.

• Hull girder and stiffened panel ultimate strength models require benchmarking

against realistic mechanical collapse data so that the distribution parameters for their

associated modelling errors may be evaluated.

• When time-variant structural degradation, such as resulting from corrosion and

fatigue, is considered, the probabilistic characteristics of such damage at any

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particular time should be quantified. While some work still continues in this area,

there exist probabilistic corrosion rates estimation models for tanker structures,

(Tanker Structure Co-Operative Forum, 1997), (Loseth et al., 1994), (Paik & Park,

1998).

• Consensus is required about the preferred methodology for determining an

appropriate return period of response for ship design and how this might be achieved

given the current status of environmental parameters and data records.

• The load factor methodology promoted in the literature is extremely promising as its

form is compatible with limit state (LRFD) design formats. Consensus is required

concerning its generality and any further development. Classification Society and

Naval experiences should be helpful in identifying load combinations to be

addressed. However, in identifying a safety format, account should be taken of

relevant ISO codes (e.g. ISO 2394) in this area.

• Target safety reliability initially requires a calibration approach to determine

appropriate values, followed by adjustments based on judgements concerning

successful design and target reliabilities in other industries, whilst recognizing that

floating structures probably need one order of magnitude (in probability of failure

terms) more reliability that comparable bottom-founded structures, and an

expectation that component and system reliabilities should differ by about one order

in probability of failure terms. In the context of longitudinally stiffened ships, plate

buckling should be treated sometimes as a serviceability limit state and sometimes

as an ultimate limit state.

• Partial factor determination will require some form of simplified modelling of

strength, loading or the reliability process in order that such determination can

proceed efficiently. Curve-or surface-fitting can be applied in all cases.

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Adeegest, L., Braathen, A., Vada, T. 1998, "Evaluation of Methods for Estimation ofExtreme Nonlinear Shif Responses based on Numerical Simulations and Model Tests",Proceedings of the 22n Symposium on Naval Hydrodynamics, Washington DC, Vol. 1,pp 70-84.

Akita, Y. 1982, "Lessons Learned from Failure and Damage of Ships", Joint Sessions 1, 8th

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Chapter 3. Critical Review ofPuhlished Work 104

Yamamoto, N. 1998, "Reliability Based Criteria for Measures to Corrosion", Proceedingsof the I1h International Conference on Offshore Mechanics and Arctic Engineering(OMAE'98), Safety and Reliability Symposium, New York USA, ASME.

Yamamoto, N., Ikegami, K. 1998, "A study on the Degradation of Coating and Corrosion ofShip's Hull Based on the Probabilistic Approach", Journal of Offshore Mechanics andArctic Engineering, ASME, Vol. 120, pp 120-128.

Yao, T., Nikolov, P. I., 1991, "Progressive Collapse Analysis of a Ship'S Hull underLongitudinal Bending", Journal of the Society of Naval Architects of Japan, Vol. 170, pp449-461.

Yao, T., Nikolov, P. I., 1992, "Progressive Collapse Analysis of a Ship's Hull underLongitudinal Bending (2nd Report)", Journal of the Society of Naval Architects of Japan,Vol. 172, pp 437-446.

Yao, T. 1993, "Analysis of Ultimate Longitudinal Strength of a Ship's Hull. Text Book ofMini-Symposium on BucklingIPlastic Collapse and Fatigue Strength; State of the Artand Future Problems", The West-Japan Soc. Naval Arch., pp 154-177, in Japanese.

Yao, T., Fujikubo, M., Kondo, K. Nagahama, S. 1994, "Progressive Collapse Behaviour ofDouble Hull Tanker under Longitudinal Bending", Proceedings of the 4th InternationalOffshore and Polar Engineering Conference (ISOPE94), Vol. VI, pp 570-577, Osaka.

Yao, T., Fujikubo, M., Varghese, B., Yamamura, K., Niho, O. 1997, "Buckling/PlasticCollapse Strength of Rectangular Plate under Combined Pressure and Thrust", Journal ofthe Society of Naval Arch. of Japan, Vol. 18, pp 561-570.

Yao, T., Niho, 0., Fujikubo, M., Varghese, B., Mizutani, K. 1997, "BucklinglUltimateStrength of Ship Bottom Plating", Proceedings of the International Conference onAdvances in Marine Structures III, Paper 28, Dunfermline UK.

Yao, T., Imayasu, E., Maeno, Y., Fujii, Y. 2004, "Influence of Warping due to VerticalShear Force on Ultimate Hull Girder Strength" Shiffbautechnische Gessellschaft, 9

th

Symposium on Practical Design of Ships and Other Floating Structures (PRADS05),Luebeck-Travemuende, Germany, pp 322-328.

Yu, L., Das, P.K., Zheng, Y. 2001, "Stepwise Response Surface Method and its Applicationin Reliability Analysis of Ship Hull Structure", zo" International Conference onOffshore Mechanics and Arctic Engineering (OMAEOl), A.S.M.E., Rio de Janeiro,Brazil.

Zhao, R., Faltinsen, O. 1993, "Water Entry of Two-Dimensional Bodies", Journal of FluidMechanics, Vol. 246, pp 593-612.

Zheng, Y., Das, P.K. 2000, "Improved Response Surface Method and its application toStiffened Plate Reliability Analysis", Engineering Structures, Elsevier SciencePublishing Ltd., Vol. 22, pp 544-551.

Moatsos, I. 2005


Appendix 3, Figures60

50

.... 40ee )0•el lO

! 10

II) 0'3:r: -10

-20

-30

- Port Dynamic-- Starboard Dynamic

,••------1'---·I •, .. .. _ ... ...e- ...... -- _.- -- -_ .....,-._------ _-----

• I• I , •,-----.------------~-----~--.--------~-~.------..---~----~------------------~---..-----• • I t~ : I I

12 Sept Oh 13 Sept Oh 14 Sept Oh IS Sept Oh 16 Sept Oh

Figure 3.1 Mean and dynamic hull stresses on a container ship (Shi et ai, 1996).

35

-Pt,

i D Pt10___....__PI, • ---~ICIIIl.--.----;--.- .. ----- ..--~-- ---~--... -Pt 3l........

... 11)( Pt~1

..._Pt7

-+-Pt3630

IS

IC

10 +-----------------------------------------~------~~~~4 • 12 16 10 0

Time Ihour)

Figure 3.2 Temperature Gradient between the Inner and Outer Walls on a container ship (Shi et ai,1996).

~ r-------------------------------------------------------------------------------------~3S ...-, .....__ . ",.", .

i!

-Outel' Wall--Innet' Wall

Q )0

I:10

12 16 20 0 4 • U 16 20 0 .. I 12 16 :w 0 .. • 12 16 20 0 5 9 13 11 21 1 S fJ .

Time (hour)Figure 3.3 Temperature readings over several days at the longitudinal bulkhead and side shell (Shi et

al.,1996).

Moatsos, l. 2005


I•• , I... -- ...... --..--------t---- _.----------- -:------------------i--···---, ~ ¥ I

• • t....-----.~----.. ----------r-----------------4------- ---- ----· , ,L---~~----~----_\.r_--~~:n~~j~ I I

504S

403S

30 ~e

2S !20 8-

EIS ~10

S

0

IS

10

e 5e• 0ee! -5:=~ -10:; -IS:x:

-20

·25Day One Day Two

-Port Mean Stress - Port Temperature

Day Three Day Four Day Five

Figure 3.4 Port Temperatures and Mean Hull Stresses (Shi et al., 1996).

s

0

·s

•to

-IS

-20 : ..

·25

SO4S

40

" U30 t...

e,. 2$ !, t 20 S."'~-i

e~ -~, t j,

IS t:.I i

-}'wtManS,_ 10

-}'wt Temperature S0

Time Interval (hour)

Figure 3.5 Mean Hull Stresses During One Day Temperature Cycle (Shi et al., 1996).

Figure 3.6 Hull thermal stresses under symmetrical (left) and asymmetrical (right) temperaturegradients (Shi et al., 1996).

Moatsos, I. 2005


O.9S~~

2020

::020

O~~~~~~~~1.0 c;6<O.85

00

Figure 3.7 Distribution of SWBM of Container Ships (Mano, 1977).

Moatsos, L 2005


Appendix 2, Tables

Author Date of Approach Comments Advantages!

Publication Limitations

Smith 1913 ExperimentaV First record of work published Work based only on

Measurements investigating thermal stresses in observations and

ships measurements with notheoretical basis

Suychiro & 1916 ExperimentaV First record of work published Work based only on

Inokuty Measurements specifically investigating thermal observations and

stresses in ships measurements with notheoretical basis

Hurst 1943 Theoretical/ First record of theoretical approach Homogeneous 2D restricted

Experimental backed by experimental beam with stresses arising

Beam investigation devoted to ship from non-linear temperature

structures. Includes deflections. distribution on unrestricteddirection

Corlett 1950 Theoretical/ Strength of materials type of Non-homogeneous beam with

Experimental analysis. Does not Include stresses occurring from any

Beam deflections change in temperature

Jasper 1955 Exact Increased accuracy theory of 2D temperature distribution.

ThermoelasticlExp elasticity approach. Includes Not valid for square holes

erimental deflections. SSC recommended with sharp comersapproach

Hechtman 1956 Exact Increased accuracy theory of 2D temperature distribution

ThermoelasticlExp elasticity approach. Includes which includes thermal

erimental deflections. Similar to Jasper stresses on boundary of

approach. openings. Not valid for squareholes with sharp corners

Meriam, Lyman, 1958 ExperimentaVFull Full scale measurements on Navy Same as above

Steidel & Brown Scale vessels analysed using the Jasper &measurements Hechtman approaches

Gatewood 1969 Review Review of state of the art in Review

thermal stress research inaeronautical engineering

Du 1991 Review Review of state of the art in Reviewthermal stress research inaeronautical/civil/marine

engineering

Heder, Josefson 1991 FEAlFull scale Thermal deformations and stresses Beam theory comparison with

& Ulvfarson measurements in OBO vessels carrying heated full scale mea~urements.

cargo Results applicable only forvessels analysed

Shi, Thompson & 1996 Full scale Investigation on double skinned FEA modelling including

Le Hire measurements! container ship & single skin bulk thermal stresses. Results

Beam bending carrier applicable only for vessels

FEA analysed

Table 3.1 Review of Thermal Stress Research since the 1900s in chronological order.

Moatsos, I. 2005



Publication LimitationsUnstifTened Plating

Faulkner 1975 Review Review of pre 1975 available Review

formulation on strength ofunstiffened panels.

Vilnay & Rockley 1981 Semi-Empirical Based on work by Frieze et al. Post buckling behaviour of

(1976) unstiffened plates whenloaded in compression. Based

on generalised effectivewidth.

Rhodes 1981 Simplified Load shortening curves of plates Good agreement with some

analytical loaded in compression. Method not numerical methods for perfect

very suitable for design purposes. plate, results for imperfectplate with initial deflectionover 30% of plate thickness

not verv satisfactory.

Chenet al. 1983 FEA Buckling and post buckling FEA modelling

strength of individual components. characteristics alwaysdebatable.

Guedes Soares 1988 Simplified Based on existing experimental and Initial deflection and residual

analytical numerical data. stress are explicitlyconsidered. Very good

agreement when comparedwith other analytical andexperimental results.

Disadvantages in calculationof maximum strength whileignoring the strain at whichmaximum values occur.

Bonnello, 1991 Semi-empirical Two characteristic points in load - With two parameters in the

Chryssanthopoulos Regression based shortening corves defined. procedure obtained from two

&Dowlinggroups of curves derived fromnumerical load-shorteningcurves, the method not verysuitable for design purposes

Davidson, 1991 FEA- Regression Unstiffened plating under in plane Limited to extent of coverage

Chapman, Smith & based compression & tension for by the data available.

Dowlingimperfect rectangular plates.

Mansour& 2004 Simplified- Design equations modelling the

Masaoka analytical ultimate compressi ve strength ofimperfect unstiffened plates.

Table 3.2 Review of Unstiffened Panels Ultimate Strength Research since the 1970s in chronologicalorder.

Moatsos, I. 2005



Publication LimitationsStiffened Plating

Faulkner 1975 Simplified semi- Based on Johnnson-Ostenfeld No consideration of lateral

analytical formulae. pressure.

Carlsen 1980 Semi-empirical Based on the Perry-Robertson No compression or lateral

formulae adopting criteria for pressure considered.

initial yielding in the outer fibres.

Bonnello, 1992 Semi -empirical Based on the Perry-Robertson Compression and lateral

Chryssanthopoulos Regression based formulae adopting criteria for pressure are considered.

&Dowling initial yielding in the outer fibres.

Smith, Davidson, 1987 FEA-Regression Stiffened plating under in plane Limited to extent of coverage

Chapman& based formulae compression & tension for by the data available.

Dowling imperfect rectangular plates.

Pu &Das 1994 Simplified semi- Extension of Faulkner's work. Limited to extent of coverage

analytical by the data available althoughit incorporates recent research

results in plate panels.

Paik & Pedersen 1994,1995 Simplified semi- Based on large deflection theory, Detailed approach on which

analytical rigid plastic analysis based on the the ALPSIULSAP wascollapse mechanism taking into originally based.

account large deformation effects.

Guedes Soares 1996 Simplified semi- Stiffened plating under in plane Good correlation with FE

analytical compression & tension for results and published tests onimperfect rectangular plates. sti ffened plates.

Paiketa/. 1997-2001 Semi-analytical Ultimate compressive strength of Good correlation with various

stiffened panels including published test data. Basis for

combined loads, edge shear and the ALPSIULSAP program.lateral pressure.

Assakkaf & Ayyub 2004 Review& Comparison of various bias and Review

Comparison uncertainty approaches for LRFDrules for stiffened panels

Egorov & 2004 Semi- Ultimate loads on ship grillages. Ultimate bending moments

Kozlyakov analyticalfFEA and pressures on grillages bytaking into account plasticbending, shear & torsion.

Steen et al. 2004 Analytical Geometrical non-linear plate Basis for the DNY PULS

theory. code which has beenvalidated against non-linearFEA, existing Class society

codes and laboratoryexperiments

Keding, Olaru & 2004 AnalyticaUISUM Developed ISUM elements FEA type of approach that

Fujikuboconsidering lateral pressure effects. reduces computational time

and requirements. Goodcorrelation with full FEA

approaches.

Table 3.3 Review of Stiffened Panels Ultimate Strength Research since the 1970s in chronological order.

Moatsos, I. 2005


Author Date of Approach Comments Advantages! LimitationsPublicati

onHull Girder

Caldwell 1965 DirectJ First attempt to theoretically Reduction in the capacity of structural membersAnalytical evaluate the ultimate hull girder beyond their US not taken into account and thus

strength of a vessel overestimating the overall USJohn 1974 Approximate First record of work published Bending moment calculation assuming wave

formula investigating ultimate strength in length equal to ship's length.ships

Smith 1977 Semi- Progressive Collapse Analysis Consideration of both geometrical and materialAnalyticallF non-linearities.

EA Problems from modelling initial imperfectionsand boundary conditions. Accurate results when

onlv the bending moment is actingOstapenko 1981 Semi- Different approach and formulation Combined applied in-plane bending and shear as

analytical from the original Caldwell work. well as combined thrust and hydraulic pressure.Strength reduction after US considered.

Nishihara 1983 Simplified Extension of Caldwell's work. Includes bi-axial bending and improved accuracySemi- Modifications that enable of the strength reduction factor.

Analytical estimation of the influence ofdamage due to grounding.

Chet et al. 1983 FEA Modelling of part of ship structure Static and dynamic FEA. Discussion onusing beam-column elements and sensitivities of US with respect to yield stress,

orthotropic plate elements. plate thickness and initial imperfection.Uedaetal. 1984 ISUM First paper published on the ISUM Development of plate and stiffened plate

method. elements simulating buckling/plastic collapsebehaviour under combined bi-axial

compression/tension and shear loads. Goodresults with any combination of

compression/tension, bending, shear and torsionloadings.

Kult et al. 1%5 FEA Modelling of part of ship structure Static and dynamic FEA. Discussion onusing beam-column elements and sensitivities of US with respect to yield stress,

orthotropic plate elements. plate thickness and initial imperfection.Maestro& 1989 Direct! Extension of Caldwell's work. Includes bi-axial bending and improved accuracyMarino Analytical Modifications that enable of the strength reduction factor.

estimation of the influence ofdamage due to grounding.

Edoetal .. 1988 Simplified Different approach and formulation Reduced level of accuracy resulting fromSemi- from the original Caldwell work. assumptions.

AnalvticalMansouret 1990 DirectJ Different approach and formulation Reduced level of accuracy resulting from

al. Analytical from the original Caldwell work assumptions.Rutherford 1990 Simplified Progressive Collapse Analysis Combination of the ultimate strength formulae&Caldwell Semi- and solution of the rigid-plastic mechanism

Analytical analvsis. Strength reduction after US considered.Paik 1990 lSUM Improvement of ISUM models. Various progressive collapse analyses and

studies.Valsgaard 1991 FEA Analysis of progressive collapse Comparative study.

et al. behaviour of models tested byMansour et al. (1990)

Gordo& 1993 Semi- Progressive Collapse Analysis Improved stress strain curves for elements.Guedes AnalyticallFSoares EAYao 1993 Semi- Progressive Collapse Analysis, Combination of elastic large deflection analysis

AnalyticallF based on work by Yao & Nikolov and the rigid plastic-mechanism analysis inEA (1991) & (]992) analvtical forms.

Bai et al. 1993 ISUM Improvement of lSUM models Development of beam element, plate element andbased on work by Ueda & Yao shear element based on the plastic node method.

(1982)Paik 1994 ISUM Improvement of ISUM models. Introduction of influence of tensile behaviour of

ISUM elements.Faulkner 1996 Modified Simplified approach for the Improvement on the Smith (1975) approach.

Smith determination of the US of a ship'shull ~irder.

Paik 1999 Semi- Progressive Collapse Analysis Improved stress strain curves for elements.AnalyticallF

EAYaoet at. 2004 Analytical Investigation on the influence of Improvement of previously proposed theoretical

warping from vert. shear force. models.

Table 3.4 Review of Hull Girder Ultimate Strength Research since the 1960s in chronological order.

Moatsos, I. 2005


Author Date of Approach Comments Advantages! Limitations

PublicationCorrosion

Southwell 1979 Regression Linear-bilinear model for design Constant corrosion rate, leading to a linear

et al. Based purposes. relationship between material loss and time.

Melchers & 1998 Theoretical/ Extensi ve theoretical and Steady state model and power approximation.

Ahammed Regression experimental investigation.Based

Yamamoto 1998 Experimental Analysis of corrosion wastage in Non-linear time dependence of time and tendency

& Ikegami Study different location for a variety of of corrosion levelling off.types of ships.

Guedes 1998 Theoretical Study on the time dependent Repair actions taken into account using constant

Soares & Approach reliability of ship hulls. corrosion rates independent of ti me.

GarbatovGuedes 1999 Theoretical Study on the time dependent Repair actions taken into account using non-

Soares & Approach reliability of ship hulls. linear general corrosion wastage model.

GarbatovPaiketal.. 2003 Regression Time-dependent corrosion The mathematical model is essentially linear and

Based/Full wastage model for the two parameters affecting the equation are

Scale FPSOsITankers based on a database of corrosion wastage

measurement measurements.

Qin&Cui 2003 Theoretical Mathematical model that can Takes into account the CPS life and thesimulate the behaviour of the interaction between the CPS and the environmentModels proposed by Melchers accelerating and decelerating phases of corrosion

(1998), Guedes Soares & once the CPS breaks down.Garbatov (1998) and Paik et al.

(2003)Melchers 2003 Theoretical/ Mathematical model for "at sea" Probabilistic model based on fundamental

Experimental immersion corrosion of mild and physiochemical corrosion. Also taking intolow alloy steels. account the process of pitting corrosion of mild

steel in a marine immersion environment.

Table 3.5 Significant Corrosion Work since the 1980s in chronological order.

Moatsos, I. 2005


Author Date of Approach Comments Advantages! Limitations

PublicationReliability Analysis

Kahn 1956 MCS Significant work published on Approximate numerical solution of the

the concept of Monte Carlo probability integral.

Simulation.

Cornell 1967 Theoretical/ Wide bound method for the Exact solution to the problem of probability of

Wide Bound determination and integration of failure but very mathematically demanding. First

Method the JPDF order approximation.

Cornell 1969 Theoretical/ Pioneering work on Reliability Probability based structural code for concrete.

CodelFORM Analysis-SORM

Stroud 1971 MCS Significant work published on Approximate numerical solution of the

the concept of Monte Carlo probability integral.

Simulation.

Hasofer & 1974 Theoretical/ Significant work on use of Exact and invariant Second Moment Code

Lind FORM- Second moment methods. Format.

SORM

Ditlevsen 1979 Theoretical/ Narrow bound method for the Exact solution to the problem of probability of

Narrow determination and integration of failure but very mathematically demanding.

Bound the JPDF Second order approximation.

Method

Angetal. 1981 TheoreticaV Attempt to determine and Higher order approximation solving the problem

Exact integrate the JPDF of increased failure modes and their correlationthat lead to loose bounds.

Shinozuka 1983 TheoreticaV Pioneering work on FORM Development of basic framework for reliability

FORM- SORM analysis analysis using FORM-SORM.

SORM

Bucher et 1990 RSM Significant contribution to the Very suitable in cases were limit state function is

al. development of RSM for known point -wisely such as in the case of FEA.

structural reliability.

Song 1992 TheoreticaV Attempt to determine and Different point evaluation as an alternative to

Exact intestate the JPDF higher order approximations.

Rajashekhar 1993 RSM Significant contribution to the Different approach to the one proposed by

& development of RSM for Bucher et al. (I990).Superior accuracy for RSM

Ellngwood structural reliability. in general but drawbacks in the experimentdesign and the identification of unknownparameters in the response function which

influence the entire algorithm.

Kim et al. 1997 RSM Use of vector projected sampling Advanced RSM algorithm.

points.

Zheng& 2000 RSM Application in stiffened plate Improved RSM algorithms.

Das reliability.

Yu, Das& 2001 RSM Application in structural Stepwise response surface method

Zheng reliability analysis of ship hullstructure.

Table 3.6 Significant Reliability Analysis Work Published since the 1950s in chronological order.

Moatsos, I. 2005


Author Date of Approach Comments Advantages! LimitationsPublication

Combinatorial Work

Manrouret 1984 Theoretical/ First significant attempt of First development of a framework for reliability

al. Analytical implementing reliability analysis of marine structures.methods to marine structures.

Masnouret 1994 Review& SSC sponsored work on Full review an demonstration of approaches

al. Demo reliability based ship-design. available and development of solid framework ofreliabilitv analvsis

Wang, Jiao 1996 PEA/Load Detailed application of Reliability of stiffened panels with consideration

&Moan Combination reliability analysis on FPSO of ultimate strength and load combination.structural units.

Paik eta/. 1997 Semi- Application on corroded tanker Closed form formulation for the determination ofempirical/ hulls. US with corrosion model based on actualFull scale measurements.

measurementWirsching, 1997 Semi- Application on corroding ship Effect of US as a function of the section modulus

Ferensic & Empirical hulls. using linear corrosion wastage model.

ThavambaliGuedes 1999 Theoretical/ Reliability of maintained ship Maintenance, fatigue and combined loading taken

Soares & Analytical hulls. into account using corrosion models as suggested

Garbatov by the authors.

Guedes 2000 Theoretical I Structural Reliability of Bulk Use of long term loading formulation and

Soares & Analytical Carriers analytical US with sensitivity study and time

Texeira variant probability of failure.

Sun&Bai 2000 Theoretical/ Time-variant reliability of ship Corrosion modelled as a time dependent randomAnalytical structures. function and SORM used to calculate the

instantaneous reliability of the primary structure.

Sun&Bai 2003 Theoretical/ Time-variant reliability of FPSO Emphasis on crack propagation and corrosion.Analytical structures. Use of Ferry-Borges for combination of

stochastic loading.

Hu&Cui 2004 PEA Investigation of effects of Taking into account effects of inspections andfatigue cracks on the tensile and repairs on stiffened panels only.compressive residual ultimate

strength.

Table 3.7 Significant Combinatorial Pubhshed Work in alphabetical order.

Moatsos, I. 2005

CHAPTER4

VESSELS & AREA DESCRIPTION & CONSIDERATIONS

4.1 Introduction

The North Sea offshore industry, established in the early 1970s, provides a significant

portion of the energy requirements of the neighbouring countries according to reports

published by the IMarEST Technical Affairs Committee (2004). Many of the major

developments are entering the twilight of their production, which has lead to divestment by

some of the major operators, and entry by independents seeking to work over existing

fields. Generally, fixed platforms are utilised in the Central and Southern North Sea. In

areas further north other developments make use of floater technology such as Tension Leg

Platforms (TLPs) and Floating Production Storage and Offloading (FPSO) solutions.

As a design solution Floating Production and Storage Offloading Vessels (FPSOs), such as

the Glas Dowr (Fig. 4.1), Triton (Fig. 4.2) Schiehallion (Fig. 4.3) and Anasuria (Fig. 4.4)

were initially used in the development of fields which are either marginal in terms of

reserves or remotely located. A "low cost" second hand tanker would be converted into a

FPSO vessel, permanently moored offshore, processing and storing crude oil produced

through sub-sea wellheads. Oil would periodically be offloaded onto shuttle tankers for

export to market. This concept eliminated the use of expensive fixed platforms and seabed

pipelines to shore based facilities in water depths up to 200m.

Advancements in design of mooring systems and sub-sea technology made FPSOs good

design options in extreme water depths and hostile weather environments. FPSOs would

provide a solution for the discovery of hydrocarbons in deep waters and also a deepwater

cost effective solution when compared with other options in terms of crude oil storage and

processing capabilities. In the last 20 years the ever-increasing numbers of operating FPSOs

worldwide (Fig. 4.5) show that not only does it provide an attractive cost-efficient design

option, but also one that is increasingly preferred over other design options such as jack-ups

(which are rarely used for oil production) and fixed platforms.

Moatsos, I. 2005

Chapter 4. Vessels & Area Description & Considerations 116

The West of Shetland area in Scotland is known as the most technically demanding in

oilfield development in the UK. FPSOs have already undertaken the challenge not only of

surviving in such a harsh region but also to provide a platform for the extraction and process

of hydrocarbon products of a lower capital cost and hopefully more profitable when

compared to other options.

4.2 The FPSO Design Concept History

Early FPSOs (Floating Production Storage and Off-loading Vessel) were simple, flat-

bottomed barges, developed for work in swampy conditions and shallow seas. As

development activity started up in less benign environments, such as the Far East and

Africa, moored ship-shaped vessels were introduced. By the early seventies, semi-

submersibles were being used for drilling in aggressive offshore conditions, and in 1974 the

first semi-submersible was converted for production duty in the North Sea in the Argyll

field. There then followed a whole series of production 'semis', both converted and new

built, for work in the North Sea, Brazil, the Gulf of Mexico, Australia and the Far East. As

FPSO technology developed, swivel and rotating turret mooring capabilities revolutionised

deployment opportunities. The first turrets were external to the hull-a few of which are still

in operation today. The development of the internal turret used the full strength of the ship's

hull to withstand heavy mooring loads and more aggressive environments. FPSOs are now

considered to be the base-case development in many situations. They are cheaper than

conventional platforms and therefore ideal for the exploitation of deep-water marginal fields

as well as small fields with short production lives. It has been suggested that while FPSO

development and deployment in the North Sea had been held up partly due to engineering

and management prejudice (with many people believing that FPSOs could not survive or

work effectively in such hazardous conditions), it had also been necessary to develop and

gain confidence in associated technology such as sub-sea trees, control systems, flexible

risers, shuttle tankers, etc. The breakthrough in the North Sea came with Amerada Hess'

Angus field. Angus was too small for a conventional platform development and too far

away from existing infrastructure for sub-sea tiebacks. The only solution was to hire a

production vessel, and the Petrojarl was converted, commissioned, and deployed in the

field for nineteen months. This fast turnaround maximised the profitability of Angus.

Twelve FPSOs are currently operating in the North Sea company (Table 4.1) and contractor

owned (Table 4.2). The change in attitude towards FPSOs in the North Sea is not just about

Moatsos, I. 2005


the advances in hardware. Commercial arrangements have also changed dramatically and

field operators/owners no longer demand sole ownership of the equipment. Amerada Hess

has been involved in FPSOs for five fields -Angus, Fife, Hudson, DurwardlDauntless and

Schiehallion -and only one was owned by the field partners. A general belief exists amongst

offshore-related companies that for practical reasons the FPSO will win the medium-term

popularity contest and become the production workhorse in many areas of the world.

With FPSOs having become a well-established development concept in offshore oil and gas

production, they have been chosen for an increasing number of field developments in recent

years (Figs. 4.5, 4.6 & 4.7). High payload capacity, short development schedule and in-built

cargo storage capacity are some important advantages that make "Ship Shaped" FPSOs very

attractive for field developers. The operation and maintenance profiles of an FPSO differ

from those of a traditional merchant ship, and those differences will significantly influence

the structural reliability of the vessel.

Both new-build FPSOs and tanker conversions have a role to play, with selection being

based on the particular field requirements. A site-specific assessment of the global structural

response must be carried out. FPSOs are designed to endure long-term deployment, often in

very harsh environment; minimum production downtime may dictate that the vessels

operate without dry-docking and survey on station. The vertical bending moment and shear

forces for a production vessel have been estimated to be approximately 30 % higher than for

a tanker with the same main particulars

4.3 FPSO Implementation of Design and Classification Regulations

Classification determines the minimum design and construction standards of a vessel. The

owner determines the required classification and under certain circumstances the owner may

request that a particular system is designed to a higher standard without altering the

classification of the vessel. Hypothetically, an owner may decide to build a vessel without

involving a Classification Society provided that the vessel will comply with both the

International Maritime Organisation (IMO) and Maritime and Coastguard Agency (MCA)

requirements. However, to meet IMO requirements regarding the flag, the vessel must be

built to Class Society Standards and failure to meet the standards set by the IMO and the

MCA will result in the vessel being impounded until the shortcomings are rectified.

Moatsos, I. 2005


Nonetheless, if the vessel is to be used as an FPSO in the UK sector, Design and

Construction Regulations (DCR) will apply according to Still (2004).

In the UK offshore sector, several operators of FPSO vessels today have the choice to

abandon classification society rules in the favour of the Offshore Installation (Design and

Construction) Regulations 1996 (DCR SI 1996/913). However, the operator, known as the

duty holder, must employ an independent body to verify his choice of the safety critical

elements that should be inspected by a third party in regular intervals. Records associated

with selection of the safety critical elements and the results of inspections carried out are

reviewed by the UK Health and Safety Executive (HSE) to ensure that the duty holder is not

in breach of the regulations. The main benefit of applying these design and construction

regulations requirements instead of classification requirements is that it allows the duty

holder to select the safety-critical elements and decide the frequency of inspections.

A series of new statutory instruments were introduced after the Piper Alpha disaster as a

consequence of the Lord Cullen Enquiry (1990) who recommended the introduction of a

safety regime offshore, which was introduced in 1992. This safety regime, referred to as the

Offshore Installations (Safety Case) Regulations (SI 1992/2885) (1992) is supported by the

following regulations according to Still (2004):

• MAR: Offshore Installations and Pipeline Works (Management and Administration

Regulations) 1995 (SI 19951738)• DCR: Offshore Installations (Design and Construction) Regulations 1996 (SI

1996/913)

• PFEER: Offshore Installations (Prevention of Fire Explosion Escape and Response)

Regulations 1995 (SI 19951743)

• PSR: Pipeline Safety Regulations 1996 (SIl996/825)

The MAR and PFEER regulations demonstrate that the management systems in place

comply with the relevant statutory health and safety provisions. The DCR scheme was

introduced to address the areas of integrity of offshore installations, well safety, and safety

of the workplace offshore and verification of safety critical items within the offshore

Moatsos, I. 2005


installation. Both fixed platforms and FPSO vessels are classed as installations since no

wellhead equipment is located on an FPSO and this party of the DCR is not applicable.

Offshore Installations and Wells (Design and Construction etc) Regulations 1996 (SI

1996/913) were introduced in 1996 and replaced the Offshore installations 1974

(Construction and Survey) Regulations (SI 1974/289) which were introduced in 1974.

FPSO vessels can either be constructed as new purpose built units, converted from an

existing tanker, or as an "interception" where a vessel slot within the shipyard programme is

purchased from a shipping company prior to or during the building of a trading tanker.

Although their hulls are constructed in accordance with classification rules, FPSO operators

may insist on inspecting critical and fatigue sensitive areas during construction, over and

above classification requirements, by their own site inspection team. Also depending on the

service conditions, the FPSO operator may request the shipyard to change both materials

and welding consumables for the outer hull to a grade that would provide better crack-arrest

properties for fatigue sensitive areas. Classification societies have developed rules for

building vessels such as trading tankers and have also introduced rules for vessels, designed

for FPSO service. In the UK, potential FPSO operators use the classification rules, in

conjunction with SI 1996/913, for the construction of new hull structures.

FPSOs operating in UK waters fall into two categories according to Still (2004): Vessel

Classification abandoned, some examples of which can be seen in the appendix (Table 4.3),

and vessel classification retained, some examples of which can also be seen in the appendix

(Table 4.4). In order for the vessel to satisfy the DCR requirements, the examination and

verification scheme is developed by the Independent Competent Body (ICB) appointed by

the duty holder. The examination and verification scheme is approved and executed by the

duty holder. It is the responsibility of the duty holder to ensure the examination and

verification is completed to the satisfaction of the ICB. Should this not be the case, an

anomaly report or verification reservation is issued. Provided the duty holder can

demonstrate to the Health and Safety Executive (HSE) that the anomaly or reservation can

be justified through an engineering route, the item will be accepted. The DCR requirements

place responsibility upon the duty holder to ensure that the vessel and topsides are

maintained in a safe condition.

Moatsos, l. 2005


4.4 FPSO Arrangements

A typical FPSO, such as the Terra Nova FPSO (Fig. 4.10), has four main topsides modules-

the M02 water injection module, the M03 separation and high-pressure compression

module, the M04 produced water/glycol module, and the M05 separation and low pressure/

medium pressure compression module. In addition to containing modules that process and

separate the oil, gas and water produced from the wells, the topsides structures also include

the turret assembly, the flare tower, the power generation module, the offloading reel, and

the platform cranes. Once reservoir fluids enter the FPSO, it moves up through the turret

and into the topsides modules. In the separation and compression modules, the fluids are

separated into oil, water and gas streams. The processed oil is then routed to the vessel's

storage tanks (Fig. 4.11), from where it will eventually be loaded onto tankers and shipped

to market. The separated water and gas streams will undergo further treatment. The

produced water will be cleaned and routed to the ocean. The gas may go back through the

turret to be re-injected into the well or reservoir to aid in oil recovery. Additionally, some of

the gas will be used to run machinery on the FPSO, such as the boilers and power

generation modules. In the event of a process upset or shutdown when the gas compressors

are not running, a small portion of the gas could be burned off through a flare tower located

at the rear of the vessel. Modules M02, M04, the flare tower and miscellaneous deck

assemblies were built at the Bull Arm Fabrication Site, where the power generation module

was also assembled. The M03 and M05 modules were constructed in Scotland. The

modules, which weigh up to 2 200 tonnes each, were lifted onto the FPSO at Bull Arm

using the heavy lift crane Asian Hercules II. Terra Nova's flare tower is among the largest

ever built, rising 100 metres from the rear deck of the vessel. In fact, a counterbalance was

required to keep the flare structure upright when it was being lifted onto the FPSO.

4.5 FPSO Storage and Offloading

Once oil moves from the reservoir into the FPSO and has been processed, the oil will be

stored within the vessel's 14 storage tanks. These tanks have a capacity ranging from over

50,000 barrels to nearly 78,000 barrels. The biggest tanks are 27m x 17m x 26m high. The

Terra Nova FPSO is double hulled - providing double containment and the oil cargo tanks

are located within the inside hull, and are surrounded by a series of ballast tanks, which

contain seawater. The FPSO's storage tanks can store up to 960,000 barrels and have a

heating system to help prevent any build up of wax in the tanks. To move oil to market from

Moatsos. I. 2005


the Terra Nova field, oil is transported by a shuttle-tanker capable of storing 850,000 barrels

of oil. However, oil must first be moved from the FPSO into the shuttle tanker via the

vessel's offloading system - designed for wave 'significant' heights of up to about five

metres (16.5 feet). When it is time to transfer oil, the shuttle tanker positions itself about 70

metres behind the FPSO. The FPSO then sends a messenger line toward the tanker.

Attached to this line is a mooring line known as the Mooring Hawser and an Offloading

Hose _ a hose 20 inches in diameter that transports the oil from the FPSO to the tanker.

Once the offloading hose is securely connected to the tanker, and the vessels meet a series

of safety checks and balances, the transfer of oil can begin. Fuel is pumped from the FPSO's

storage tanks into two export pipes, through the export line to the Offloading Hose. Crude

flows through the Offloading Hose at a rate of up to 50,000 barrels per hour. During the

transfer, the oil passes through what is known as the Export Oil Fiscal Metering Package.

This allows the Terra Nova owners to calculate the amount of crude offloaded and available

for sale in the market. It will take about 24 hours to transfer a full load of crude from the

FPSO to the tanker.

4.6 The North Sea

The North Sea may be considered a semi-closed basin with the European landmass and

United Kingdom providing east and west boundaries, and the English Channel a restricted

entrance at its southern extremity. Broadly speaking the North Sea may be split into three

regions with regard to Met-Ocean conditions; The Northern North Sea (NNS), Central

North Sea (CNS) and Southern North Sea (SNS). Such a set of regions is also consistent

with the three major groupings of oil and gas developments and the bathymetric properties.

For the latter the SNS can be considered to have depths less than 50m, the CNS depths of

50-100m and the NNS depths greater than 100m. A deep trench, The Rinne, is also present

in the NNS along the coast of Norway.

4.6.1 Geographical Territory of the West of Shetland

The area referred to in this thesis as "West of Shetland" stretches between the Shetland and

Orkney Islands, North if the Scottish mainland, to the Faroe Islands, some 450 km to the

North West. The area is split between UK and Faroese designated waters (to the South-East

and North-West respectively) with a zone in the middle, known as the 'White Zone' (Fig

4.10) which is still in contention between the two Governments and therefore effectively

Moatsos, 1. 2005


unavailable to the industry for exploration. The vast majority of the offshore related

activities such as exploration, drilling and all oil discoveries to date have been made in UK

waters. In the last 3 years, BP and Shell activities have been focused on the Southern end of

the Basin.

Characteristic of the Faroe Shetland area is the relatively deep water with water depths to

200 meters extending some 100-150 km to the North-West of the Shetland Orkney Islands.

Thereafter the sea bed deepens quite steeply reaching a maximum of about 1200 metres in

the centre of the Faroe-Shetland Trough before rising again towards the Faroe Islands.

These are considerably greater than in the North Sea where the deepest water development

in the Norwegian sector is Troll at some 320 metres and UK sector is Magus at less than

200 metres.

4.6.2 Environmental Apprehension

Bird colonies are of international importance on the Shetlands and Orkney. Islands with

many designated areas of scientific interest and naturally beauty which will be at risk in the

case of produce water discharge, disposal of cuttings and hydrocarbon emissions. All these

factors have also led to the key concern of oil spills. With wind and currents presence oil

spills could beach on either Shetland or Orkney. In the case of the North Sea, on the other

hand, any oil spill would tend to move away from the land to North-East open waters.

Specifically in the case of the Shetland Island, susceptibility to oil spills has magnified as a

result of the Braer incident in January 1993 on the southern coast of Shetland, where 85000

tonnes of light crude oil were spilled in a severe storm. The macrocosm of the oil fields

West of Shetland is of high wax content, therefore in the case of an oil spill if it is not

treated rapidly with dispersant, a form of emulsion will be formed which would prove lethal

to the underwater flora and fauna of the area.

Primarily oil production activity planning and operations include processes that minimize

the risk of any oil spill through design and operations procedures and through arrangements

that would efficiently handle any oil spills that might occur.

Moatsos, I. 2005


4.6.3 Met-Ocean Conditions

The metocean conditions in this particular area are recognised as one of the most severe

globally in which the industry is operating. Long swells, rapidly changing weather

conditions and complex current regimes characterise the area. From BP's design criteria for

Foinaven of 100 year return conditions, wind speed of 40 m/s and significant wave height

Hs of 18 meters the extreme nature of the sea conditions that are typically present in the

area can be seen, however these conditions are not significantly greater that the ones present

in the North Sea.

Analysis of current measurements by BP revealed large variations in design current speed

with location. Severity of the metocean conditions in water depths in excess of 500 meters

made BP suspend an exploration well in 830 meters of water, due to combined forces being

exerted on the rig by the wind, waves and currents that made station keeping extremely

difficult.

Although improvements exist in our cognition, a multitude of uncertainties still exists on

metocean parameters and efforts are continuing from various sources in the industry to meet

the challenges in this distinctive area.

4.7 Typical Field history - Schiehallion field

Schiehallion was discovered in late 1993 by BP and the field lies some 15km to the east of

Foinaven in somewhat shallower water (350-400m). The field rides on the boundary

between block 204/20 (BP and Shell) and Block 204/25b (held by Amerada, Aran, Murphy

and OMV). There are minor extensions into three adjacent Blocks (all held by BP and

Shell). The first exploration well drilled suing 3D seismic techniques was acquired after the

discovery of Foinaven. In the spring of 1994, the extension of Schiehallion to the South into

the Amerada operated Block 204125a was proved by well 204/25a-2. A Northern satellite

known as Loyal was drilled and proved at the end of 1994 lying wholly within the BP/Shell

Block 204/20 but plans exist for that to be in development in parallel with the main

Schiehallion field.

In 1994 and 1995, six appraisal wells were drilled together with a horizontal well which was

subject to an EWT and proved to be the most productive well drilled to date in the West

Moatsos, I. 2005

Chapter 4. Vessels & Area Description & Considerations124

Shetland province. From a 60 day test, flow rates in excess of 20,000 barrels per day (bpd)

were recorded and 714,000 Barrels (bbl) of oil were recovered. This verified the value of

dynamic data in appraising a field for development by EWT on Schiehallion.

Geologically, Schiehallion's reservoir is of superior quality than Foinaven albeit complex in

structure. Faulting is less severe and reservoir communication is excellent throughout. The

oil is similar in nature to Foinaven with API gravity of 26°C, Gas Oil Ratio (GOR) of 340

scflbbl., wax content 7-11%, viscosity 3.4 cps. As a result of the better reservoir quality and

the absence of a gas cap, a higher recovery factor is anticipated. On the other hand Loyal is

a younger, but deeper, reservoir similar to both Foinaven and Schiehallion, but noticeably

smaller. Consequently the collective reserves of Schiehallion and Loyal are in the range of

250-500 mmbbls.

Utilization plans for Schiehallion, concerning 29 subsea wells comprised of 22 wells on

Schiehallion, 6 wells on Loyal plus a gas injector including 16 producers and 12 water

injector from four main drilling centres, 3 for Schiehallion and 1 for Loyal, production

through an FPSO and export by shuttle tanker, which was the same conceptually as

Foinaven but to some extent bigger. Horizontal producers and multi-lateral wells were

planned and produced gas is re-injected to reduce emissions as part of BP's initiative.

Volatile Organic Compound (VaC) emission is also reduced through the use of a displaced

gas recycling system when transferring production to the offloading shuttle tanker. The

FPSO is designed for a production rate of 142,000 bpd. The Schiehallion FPSO with a

storage capacity of 892,800 bbls is one of the biggest FPSO's in the world.

4.8 Description of VesselsAnalysed

For the purposes of this research 3 FPSO vessels were selected to be analysed of different

structural configurations but also ranging from new built vessels to tanker conversions. The

three individual design approaches would represent the variety of FPSO configurations

operating worldwide but specifically in the North Sea.

TritonThe first vessel, of which structural and operational details were available for analysis, was

the Amerada Hess/Shell jointly owned and operated Triton FPSO. The vessel was originally

Moatsos, I. 2005


built as a tanker and was later converted to an FPSO and as a result of that has a structural

arrangement that is closer to that of a conventional tanker with double bottom, side and

hopper tanks. The entire structure is built from Grade AH high tensile steel with the

exception of the inner bottom and areas close to the neutral axis. Very limited data on its

design characteristics and operational profiles was available and it was assumed that they

follow similar patterns as the other two FPSOs for which a large wealth of information was

available. The Bittern field has been developed as part of the Triton Development Project in

conjunction with Shell and the owners of the Guillemot West and North West fields. Bittern

is located 118 miles east of Aberdeen in Blocks 29/1a & b and was discovered in 1996.

The fields are produced via an array of subsea infrastructure and the Triton FPSO. Oil

export is via shuttle tankers and gas export via the Fulmar pipeline to St Fergus. The FPSO

Triton was installed on location in March 2000 and first oil achieved just four weeks later

on 15th April. Plateau production from Bittern is expected to be approx. 60,000 barrels/day.

AnasuriaThe second vessel, of which structural and operational details were available for analysis,

was the Shell UK owned and operated Anasuria FPSO. The vessel is a purpose built FPSO

and as a result of that has a structural arrangement with single bottom and side tanks. The

entire structure is built from Grade DH high tensile steel with the exception of areas close to

the neutral axis and the majority of the longitudinal stiffening. A large wealth of

information was made available to the author through the generous cooperation of Shell UK

and the Health and Safety Executive (HSE) describing its design and operational

characteristics.

Anasuria is the first purpose-built floating production storage and offloading (FPSO) vessel

to be constructed for Shell UK Exploration and Production (Shell ExPro) in the UK North

Sea. The vessel was designed and constructed by Mitsubishi Heavy Industries (MHI) in

Nagasaki, for the combined development of the Teal, Teal South and Guillemot A fields.

The well stream enters the vessel through a swivel and is offloaded to shuttle tankers using a

stern mooring system. The structure consists of seven cargo tanks, which can store 850,000

barrels, and two slop tanks surrounded by ballast tanks. The tanks are formed by

longitudinal and transverse bulkheads, including a longitudinal centreline wash bulkhead.

Moatsos, 1. 2005


The hull has a single bottom for protection of the cargo tanks - particularly against collision

damage from moored shuttle tankers. Strong points were welded on to the structural

interface between topsides and vessel deck. allowing topsides pillar supports to be included.

The topsides facilities were designed as separate modules. Amec used the largest single

pedestal crane in Europe. a PC9600 from Grayston, White and Sparrow. to lift two modules

a day, including the 555t lower section of the turret and the 340t switch-gear module. The

twelve mooring lines are anchored to the seabed by piles in six pairs.

Pumping is carried out by hydraulically-driven, 1400m3 per hour cargo pumps, powered by

high-voltage motors. When offloading, four pumps are used simultaneously (5,600m3 per

hour). Inert gas supply and tank purging closed systems obviate the release of tank gas on

the maindeck area. The topside process design consists of a conventional three-stage crude

oil stabilisation train. Wellhead fluids are received separately by two identical first-stage

separators, each designed to cater for 55,OOObpd.The associated gas is dehydrated and

compressed prior to export. Produced water is treated to an oil-in-water specification of

20ppm by means of hydrocyclones. The separators are aligned parallel with the vessel's

longitudinal axis and located amidships, where pitch and heave accelerations are lowest.

The stabilised crude is routed to the wet crude reception tank for final dehydration prior to

storage. Water injection facilities are provided to inject treated seawater for reservoir

pressure maintenance. The turret and swivel anchor the facility to the seabed, acting as the

entry point for the well fluids and the exit points for gas exports and water injection.

Schiehallion

The third vessel, of which structural and operational details were available for analysis, was

the BP owned and operated Schiehallion FPSO. The vessel is a purpose built FPSO and as a

result of that has a structural arrangement with single bottom and side tanks. The entire

structure is built from Grade DH high tensile steel with the exception of areas close to the

neutral axis and the majority of the longitudinal stiffening. A large wealth of information

was made available to the author through departmental involvement in various

investigations examining design characteristics of the particular FPSO describing its design

and operation. The Schiehallion is the world's largest new build vessel of its type and is

capable of processing around 150,000 barrels of oil a day and storing 900,000 barrels of oil.

The smaller Petrojarl Foinaven can process up to 120,000 barrels of oil a day and store

around 280,000 barrels of oil. Both the Petrojarl Foinaven and the Schiehallion FPSOs have

Moatsos, I.2005


been specially designed to withstand the harsh climates of areas like the Atlantic Margin.

Extreme conditions have been encountered over the past few years of operating experience -

with a fifty year wave of 27 metres in February 1997 and the tail-end of hurricane Mitch in

November 1998 - which have contributed to improving our knowledge and procedures for

operating safely.

Structural arrangements and configurations for all three vessels can be found in the

Appendix (Fig 4.14, Fig 4.15 & Fig 4.16) along with principal particulars and operational

details (Table 4.5). The sectional properties of all three vessels were calculated for their as-

built condition to be used in later stages of the research using a FORTRAN90 based, author

developed code and validated using the CSSP software developed by Prof. P.K. Das of the

Dept. of Naval Architecture and Marine Engineering of the Universities of Glasgow and

Strathclyde. Results of the analysis can be found for all three vessels in the Appendix (Table

4.6). The results reflect the difference in structural arrangements, scantlings and size of the

vessels.

4.9 Discussion-Remarks

The recently published third edition of the World Floating Production Report, by Douglas-

Westwood Ltd, the UK based energy industry analyst, forecasts strong growth in the

demand for floating production systems over the next five years. There are proposals for

FPSOs which incorporate drilling facilities (FPDSOs), which are intended for deployment

in remote and/or harsh environments. Although the FPDSO concept has certain attractions,

there are no indications that it will be adopted in the near future. Recently, the FPS sector

has been affected by a number of factors, both intrinsic and extrinsic, which have had

repercussions on the market at both regional and global levels. These include:

• Structural changes in the UK sector of the North Sea, where increases in the

industry's tax burden have been coupled with indications that some oil majors are

re-assessing their positions in the light of potentially more lucrative opportunities

elsewhere.• Political change in Brazil in the wake of the election of a left-leaning president, has

led to a tightening of local content requirements which have contributed to the slow

progress of some significant projects.

Moatsos, I.2005


• A number of very experienced offshore contractors have fared badly on large-scale

deepwater turnkey EPIC projects. The suitability of lump-sum contracts in such

high-cost and technically challenging contexts is increasingly being called into

question.

Projects valued at more than US$4biIIion (£2.5 billion) are likely during the period 2003-

2007. FPSOs represent an ever-larger share of the market (Fig. 4.17) The four main drivers

behind the continued demand growth within the FPS sector today are:

• Continuing expansion in the use of subsea production technologies.

• The industry's move into deep water areas.

• Exploitation of marginal fields

• Growing emphasis on fast-track and/or phased developments.

In terms of market value, the world's three major deepwater regions, Africa, North

America, and Latin America, account for three-quarters of the forecast global expenditure.

The relatively benign environments and shallow waters in which most FPS prospects in

Asia are located will enable the adoption of cheaper FPS solutions.

Moatsos, I.2005



Bluewater Energy Services Website [Online. Internet] Available: http://www.bluewater-offshore.com, Accessed: July 2005.

BP Website [Online. Internet] Available: http://www.BP.com ,Accessed: July 2005.

Chua, Chung-San 1997, "Optimum FPSO Design for West of Shetland", Final Year Project,University of Glasgow, Department of Naval Architecture and Ocean Engineering,NAOE-97-03

Douglas-Westwood Ltd. 2003, "The World Floating Production Report III (2003-2007)",Douglas- Westwood Ltd, Kent, UK.

HESS Website [Online. Internet] Available: http://Hess.com ,Accessed: July 2005.

IMarEST Technical Affairs Committee 2004, "Met-Ocean features in the North Sea", TheJournal of Offshore Technology, Vol. 12, No.2, March/April, pp 32-35.

Lloyd's Ship Manager, (June 1994-July 1996) Periodical.

Maritime Research Institute of Netherlands Wageningen Website [Online. Internet]Available: http://www.marin.nl/. Accessed: July 2005.

Offshore Engineer, (May 1995-Sept. 1996) Periodical.

Offshore Technology Website [Online. Internet] Available: http://www.offshore-technology.com , Accessed: July 2005.

SHELL Website [Online. Internet] Available: http://www.shell.com, Accessed: July 2005.

Ship Technology Website [Online. Internet] Available: http://wwwship-technology.com ,Accessed: July 2005.

STATOILMagazine, (1994-1996), Issues No. 1-4, Periodical.

STATOIL Website [Online. Internet] Available: http://www.Statoi1.com , Accessed: July2005.

Still, J. 2004, "FPSO Hull Structures - All Change to New UK Regulations?" The NavalArchitect, The Royal Institution of Naval Architects (RINA), pp 41-44.

The Offshore Installations (Safety Case) Regulations 1992, SI 1992/2885, HMSO, ISBN011025869 X.

The Society of Petroleum Engineers Website [Online. Internet] Available: http://www.spe-uk.org/index.htm, Accessed: July 2005.

Terra Nova Project Website [Online. Internet] Available: http://www.terranovaproject.com.Accessed: July 2005.

UK Department of Energy 1990, "The Public Enquiry into the Piper Alpha Disaster (CullenReport)", Cm 1310, HMSO, ISBN 010113102 X, 2 Volumes.

Whitehead, H. 1993, An A-Z of Offshore Oil and Gas, Gulf Publishing Company, Houston,USA.

Moatsos, I.2005

http://www.BP.com

http://Hess.com

http://www.marin.nl/.

http://www.shell.com,

http://wwwship-technology.com

http://www.Statoi1.com

http://www.terranovaproject.com.


Appendix 4, Figures

Figure 4.1 The 'Glas Dowr' FPSO. (Marin, 2005).

Figure 4.2 The 'Triton' FPSO (Hess, 2005)

Figure 4.3 The 'Schiehallion' FPSO (Shell, 2005)

Moatsos, I. 200S

Chapter 4. Vessels & Area Description & Considerations l31

Figure 4.4 'Anasuria' FPSO (Mitsubishi Heavy Industries Ltd, 2005)

10

to

II

~

......-: ( I

III !

I /J

~ t---V 1-er--- I

I I~ ___ moI~boKinds I

70

60

so

30

10

o1915 1917 1989 1991 1993 t~ t991 1999 _t

NoI&: Fleet totIIs for 1991-1001 Include FPSOs comnoIUedtor construction as of IUy 1998 i..e. DO pfOjection tor fuIuno,owtII willi rapcct 10 otdcts pI.Ked in 1999-1001.

Prcp¥l:d "y • __ tM.c~ 14, 1000

Figure 4.5 Growth in the World's FPSO Fleet 1985-2001, (Bluewater 2005)

Moatsos, I. 2005


bluewaterPropnd ~ ~ IIIrCh 14, 1000

Figure 4.6 Distribution of the World's FPSO Fleet, (Bluewater 2005)

(ontractorOwn2d

. Contractor Own«!

Rest of Wot1d

Prepared by BloewatCH'March 24, 2000

Figure 4.7 FPSO Ownership, (Bluewater 2005)

Moatsos, I. 2005


It is widely used n the Iltemational oil and gas Industry. Now. noafing produClion technology i.beCO<Tlltlgpart of openationson the Grand Bank. of NlI'Nfoundiand. Terra Nova's purpo.e-bui~Floating. Production. Stor.ogeand OfIIoading V"Me' (FPSO) is due to begin cperauons next year.In tius tSSUit. we conlinue a senes of articles on how Tetrl Nova's, FPSO works. featUring someof the vessel's ey systems and cofT1)Onents.

flanTOI

w....l't~..

Turret Ate. Atcornmodat,on1'0& Helideck

The FPSO has lout main IOpsidesmodules. andseveral other components. Here the various pansof the vessel ate hoghtighted from stem to stem.

Figure 4.8 Terra Nova FPSO Deck and operational arrangements, (Terra Nova Project, 2005)

It is Widely used In the International 011and gas industry Now, "oating pmducrion technoklgy isbecomongpan of operations on the Grand Banks of ew1oundland. Torra Nova's purpcse-bul~Floating, Production, Storage and OfIIoading veMei (FPSO) is due 10 begin operations next year.In th.. issue, we continue a seties of anides on how Terra Nova's FPSO wotlls, featuring someof the veuel's ay systems and components.

Offloading Ho••

\..

~~~ ..~---.To Shuttle

Tanker

Below: An illustration of how a shuUle tanker ... 11receive oi from lIle FPSO, Left. An internal viewof Ih. FPSO's storage tanks

Figure 4.9 Terra Nova FPSO Omoading operational arrangements, (Terra Nova Project, 2005)

The Terra Nova FPSO uses a tandem stem oiftoadingsystem Oil WIllbe transferred 10an 011tanker VIaa speciallydes gned oftloading hose at lIIe rear of the FPSO.

Moatsos, I. 2005


.~.....3'" l'

.. .. 4' ~

"

.\",..~~

.

.':

.'

' ....~.~ .

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1 .FAROEISLANDS'.

,."

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.: ', ~ ~ .',' .~, :~~ ,<":':""",-."

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..... I

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.' "r .,.Figure 4.10 The West of Shetland area of Scotland.

Moatsos, 1. 2005


Environmental Characteristic

West of Shetland

S)40.0mIsNorth Sea

Figure 4.11 Environmental characteristics comparison of the West of Shetland and the North Sea.

Foinaven, Schiehallion & Loyal

o

2WIH·

205/16

204/20-4.

Schiehallion

•Z04I251-3

Figure 4.12 The Foinaven, Schiehallion and Loyal fields.

Moatsos, 1. 2005


.$..t!.N.tai.~_ .....lt;;.~_.!'!r.,!tl!_.. ... '.n""ft! t~ ..--.--~-

.&UL..).~_~!,!.,!,~·'''·!'r'T··'HJ!!,.l..l.Ul--"J.~,_- ....- ...--

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Figure 4.13 Anasuria FPSO Structural Details & Configuration.

"'~"".'."!"W;".J,:~~'~~".TI'/~:;r~=fk!;'~

>'! • ..!ll:E '_J:!

J\~::::~~il-\< !~._ •• ~." •• "l~~'1:" .------

.:£=~-",../' ~~.!:'::.

Figure 4.14 Schiehallion FPSO Structural Details & Configuration.

Moatsos, 1. 2005


ORDINARY SE9T10N ::.<

Figure 4.15 Triton FPSO Structural Details & Configuration.

Figure 4.16 Future FPSO Installations, (Douglas-Westwood, 2003).

Moatsos, I.2005


Appendix 4, Tables

North Sea, oil company owned (total of 9)

Vessel Name Entered 0'Ml8r Origin Current Lee. Status Prod. cap., Dead..i1 Siorage cap., bbI

service bopd

Gryphon A 1993 Kerr McGee newbuild Gryphon, UK 112 Kerr McGee 1993 working 120,000 87,000 527,100

Anasuria 1996 Shell newbuild TeaV 90 Shell 1996 working 85,000 129,550 850,500Guillemot. UK

Captain FPSO 1996 Texaco newbuild Captain, UK 104 Texaco 1996 working 60,000 114,000 540,000

Nome 1997 Staloil newbuild Nome, NorMIY 380 Staloil 1997 working 170,000 97,000 724,000

SchiehBJlion 1998 B.P newbuild Schiehallion, UK 400 BP 1997 working 142,000 154,000 892,800

AsgarcJAFPSO 1998 Statoil newbuild Asgard, NorNay 300 Staloil 1998 working 175,000 175,000 950,000

JotunFPSO 1999 Esso Norge newbuild Jotun, NOrMIY 126 Esso Norge 1999 working 92,800 585,000

8a/d8rFPU 1999 Esso Norge newbuild Balder, NOrMIY 126 Esso Norge 1997 working 98,700 86,700 380,000

Triton 1999 Amerada newbuild Bittem, UK 188 Am. 1999 conSlructiHess/Shell Hess/Shell on

Table 4.1 Table of Oil Company owned FPSOs operating/planned to operate in the North Sea,(Bluewater, 1999).

North Sea, contractor owned [total of 10)

--- 0.0- OrIgIn a.- w_ Opor-. -.- ~ ........ ........f'eboiorll 1_ PGS -_,UK 14 Ivoo 1095 WOIIdng 60,000 31,413 191,000

UisgeGonn 1995 Bluewater conversfm Fde. Fergus & 70 AmeIada Hess &95 wodc.ing 50,000 100.000 616,000Flora UK

_s- 1981 - ...- MacruIocI1, 150 Ccnoco 1091 ~ 60,000 98,224 550,000,,_ UK

GlasDowr 1991 BlU6'W8ter ...-av_

95 Amerada Hess 3/97 available 50.000 105.000 640,000

PotrojatIFoina_ 1981 PGS COftV'8I'Iion Forev..,lJ( 461 BP 2091 WOIIdng 140,000 302,000

_eun- 1981 - ...- ~,lJI( 78 - 4091 _..., 55,000 100,000 560,000

81eoHo/m 1991 Btuewater

ne_Aoss~ 100 TalIsnaMlG 3091Ross wOO<mg 100,000 105,000 660,000

UK 2001 Blake

HcsweneSnm 1997 ~ nAwbuild ?terce,Ut< 85 Enterpnse 1997 working 70.000 103.000 650,000

BanlrFPSO 1_ P.G.S. - _,U.K. 100 Canoco 1_ wod<ing 60,000 20,000 120.000

PotrojatIV-v 1_ P.G.S. -V_~ ~ WOIIdng 60,000 450,000

Table 4.2 Table of Contractor owned FPSOs operating/planned to operate in the North Sea, (Bluewater,1999).

Moatsos, I. 2005


OPERATOR VESSEL REMARKS

Shell Expro Anasuria UKForeign Office advised the owner to classthe vessel. This action was to provideprotection for the vessel if attached during

transit.On arrival at Tyneside for fittingout process facilities, the classwas dropped.No propulsion installed

BP Exploration Schiehallion No propulsion installed

Amerada Hess Triton 1 Engines removed

ChevronTexaco North Sea Captain FPSO No propulsion installed

Table 4.3 Classification Abandoned Examples, (Still, 2004).

Owner - Vessel Operator Oilfield Vessel

PGS - Conoeo Phillips Banff Ram/arm Banff '" A

Bluewater - Shell Expro Pierce Haewene Brim .. A

Bluewater - Amerada Hess Fife, Fergus, Flora & Angus Uisge Gorm '" A

Bluewater - Talisman Energy Ross, Parry & Blake Bleo Holm" A

A P MOller· Canadian Natural Resources Curlew & Kyle Maersk Curlew" A

NSPC • ConocoPhillips MacCuUoeh North SeaProducer" A

PGS - BP Expro Foinaven Pertrojarl Foinoven .. A

Kerr McGee Gryphon Gryphon A A

Kerr McGee leaden Global Producer 111 A

.. \""",-",dsowl'k.'(.ltty non-o!>sct ~)WI'k!'r:>an! jccsed lO the .L~,;;d opeeuor ,t:.r pt'otJuclion purpo:st:s and :.U\: retained in classilication as IIcouduioo

ofthe mOf1S.;SI!. Mortg3~e I.:ondilion -, are dh.:talni h) J 00n\. ullowmg it to :K°UIhl.· vessel in the event ,h.;Jt the owner ':1K:~lItnh:~r .. tim1lK.:lai

difficulties.

" These vessels have retained their propul5ion machinery

Table 4.4 Classification Retained Examples, (Still 2004).

Main Paritculars TRITON ANASURIA SCHIEHALLION

i: 233 m 225.8 m 228.4 m

Lscant 230.375 m 219.026 m 227.756 m

B 42 m 44.8 m 45 m

D 21.3 m 23.8 m 27.25 m

ddesil!n 13.6 m 16.65 m 20 m

dscant 14.7 m 16.8 m 20 m

Cb 0.91 m 0.9617 m 0.911 m

Tonnage 105000 OWT 129550 OWT 154000 OWT

Capacity 630000 bbls 850500 bbls 1000000 bbls

Production per 105000 Bopd 85000 Bopd 142000 Bopd

dayProduction 6 days 10 days 7 days

cycleOjJ1oading 5 days 9 days 6 days

everyTsw.full 73 days/year 73 days/year 73 days/year

Tswfull 24 hours 24 hours 24 hours

nswfuJl 73 hours 73 hours 73 hours

Table 4.5 FPSO Principal & Operational Particulars.

Moatsos, I. 2005


TRITON ANASURIA SCHIEHALLION

Structural 5.8089*106 mm2 6.2955*106 mm" 7.8274*106 mm"

AreaElastic C. 9.4349 m 11.617 m 12.622 m

Zco-ord.2ndMom zz 1.2099*10'J mm" 1.5474*109 mm" 1.9328*10'J mm4

2ndMom yy 4.0166*1O~ mm" 5.6532*1O~ mm" 8.7603*lcf mm4

Shear C. Z -3.5236 m 12.020 m 9.6640 m

co-ord.zz Shear 1.3427*1OD mm" 1.8523*10° mm" 2.0122*10° mmT

Areayy Shear 1.1315*1OD mm" 1.6246*10° mm" 1.7160* 1()o mm2

AreaTorsional 2.7297*108 7.8950*108 9.8046*10l!

ConstantTable 4.6 FPSO Midhsip Section Properties-As Built Condition.

Moatsos, I. 2005

CHAPTER5

THERMAL STRESS ON SHIP STRUCTURES

5. 1 Introduction

Having examined the history and approaches of thermal effects in ship structures in

(Chapter 3), and the nature of the problem of Global Warming in (Chapter 2) now it seems

suitable to examine the ways in which we can model our problem in more detail and

investigate the effects of diurnal temperature changes and the best way of mathematically

modelling such phenomena. The Naval Architect is interested principally in five aspects of

temperature effects in ships:

1. Temperature gradients in the hull- their shape and magnitude.

2. Deflections of the hull girder caused by thermal expansion.

3. Thermal Stresses in the hull structure.

4. Buckling of the hull plating resulting from thermal expansion

5. Contribution of thermal stresses to brittle fracture

With the issue of diurnal temperature anomalies and global climate change already

discussed in (Chapter 1) and (Chapter 2) of this thesis, the question arises of how we can

accurately model mathematically such phenomena and their effects on marine structures.

5.2 Terminology

It would be useful in this point to describe thermal stress terminology which will be

extensively used throughout this chapter. The phrase "temperature distribution" is used in

this thesis to describe the temperatures at a given time at selected points of the structure and

the term "thermal stress" refers to the changes in stress which are computed from an actual

or an assumed temperature distribution. The algebraic signs given the thermal stress indicate

the direction of the change and do not describe the nature of the stress, tension or

compression, unless the initial temperature condition was accompanied by a zero stress.

"Insolation" is the rate of solar radiation striking an exposed surface.

Moatsos, I. 2005

Chapter 5. Thermal Stress 142

5.3 Temperature conditions in ship structures and their effects

As mentioned in (Chapter 3), containing the critical review of this thesis, the problem of the

stresses set up by the temperature gradients under normal operating conditions is common

to all ships. The effects of temperature are threefold according to Miller (1961):

4. Temperature changes cause a deflection of the hull

5. Temperature change can result in the properties of the material of the hull girder to

change

6. Temperature resultant stresses are generated

When it comes to taking into account temperature effects on ship structures the main

problem confronting designers is that of determining the maximum service temperature

changes and related temperature distributions that could occur during a ship's lifetime.

These difficulties arise from the fact that the ship's structure temperature at any given point

is sensitive to the ship's environmental conditions that can change between hours, days and

seasons. This leads to the simple conclusion that the structural temperature of a ship must

also continuously change in somewhat the same manner. Unfortunately ship designers have

little or no control over factors such as changes in weather, climate and service conditions

that can influence ship design.

In thermal analysis of structures, temperature difference is the most important factor. In the

case of a ship's structure, as a result of the structure's size and complexity a large number of

such temperature differences can occur that can also vary between different parts of the

ship. A set of temperature conditions that can give rise to a significant temperature

difference in one segment of the ship's structure may not necessarily be the same set of

temperature conditions that will create the most adverse temperature difference for another

segment of the vessel.

5.4 Temperatures prevailing at times of casualties

5.4.1 Deflection

If the temperature change over the whole hull is uniform or if it consists of a linear gradient,

then the hull will change in volume or will bend or both with stresses not being present.

Moatsos, I. 2005


Such conditions are unlikely to arise in ships and generally the temperature gradients will be

such that stresses will always coexist with the deflection.

5.4.2 Change in the Properties of the Material

According to an extensive literature review by Meikle & Binning (1961) as described in

Miller (1961) test data indicates that for a wide range in steels the change in Young's

Modulus E is nearly linear with change in temperature in the range of OnCto SO°C, the rate

of decline with increase of temperature being of the order of 0.760MNI (m2S0tonlin2) per

10°C. No data is available on the effect of Shear Modulus G but it is believed that Poisson's

ratio increases with increasing temperature, so that it is to be expected that the effect on G

will be greater than the effect on E. Of greater importance in our case is the increase in

ultimate strength as the temperature rises so that at 200°C the ultimate strength has

increased by 2S%. The change in 0.1 % proof stress is much less but also shows slight

increase up to 200°C. This effect is due to the strain hardening which is imparted by the

applied stress coupled with the "thermal hardening" effect of the elevated temperature. The

coefficient of thermal expansion of mild steel increases with increase in temperature from a

value of approximately 11.92xl0-6 per -c at OnCto approximately 7.7xl0-6 at 260°C. These

changes are not affected by the time of heating and unfortunately no information on fatigue

strength in the range of SO-SOO°Ccould be found.

Mounce, Crossett & Armstrong (19S9) reported on the properties of steel suitable for the

containment of liquid gases down to -270°C but in the case of this study such data was not

of use. Similarly in the case of aluminium alloys under high temperatures, the effects are

considered to be much more complicated but since aluminium is not likely to be used in the

solution of marine high temperature problems such issues have not been investigated in this

thesis and are not being discussed.

5.5 Temperature Stresses

According to Hechtman (19S6), if we examine the conditions which existed at the time of

failure of a large number of ships we can safely say that temperature stresses would have

been present to a considerable degree in about SO% of the cases examined. After careful

examination of that study we can deduce that factors causing temperature stresses are:

Moatsos, I. 2005


1. Localised artificially induced temperature change.

a. Heating of fuel oil in the double bottom of transversely framed ships

(Maximum temperature 55°C).

b. Heating of liquid cargo in tankers. If we examine cargo handling practices

since the 60s (Miller. 1961). the temperature of oil cargo during loading may

be higher than at sea and may reach 71°C. Before pumping the oil cargo

temperature may be raised to as high as 57°C.

c. Cleaning with boiling water of liquid cargo spaces in tankers (maximum

temperatures used can reach 99°C although the recommended is 74°C).

d. Refrigeration of cargo spaces in dry cargo ships (Temperatures of -20°C).

e. Loading or discharging liquid cargo or ballast (Maximum temperature of oil

would appear to be about 71°C).

2. Rapid Change in water temperature. An example described by Miller (1961) lists

that in waters bounding Gulf Stream off the American coast this would amount to a

16.5°C temperature change in about six hours sailing.

3. Rapid change in air temperature. Again from (Miller. 1961) recorded temperature

drops at time of casualties would range from 8°C to 20°C.

4. Temperature of air well below that of water. No specific data is given by Miller

(1961) or Hechtman (1956) for specific casualties but a figure of +/- 35°C maximum

variation of air from water temperature would appear reasonable.

5. Sunshine on the side of the vessel only in northern latitudes on winter mornings.

Due to insolation in combination with albedo effects (reflection from sea surface).

the steel temperature. if it is painted black. may be 35°-45°C higher than the air

temperature. This is the maximum that could occur in still air and this figure is

affected by the atmospheric conditions. losses by convection. conduction and

radiation to surrounding media. the heat capacity of the structures and the colour of

the paint used. No data is available on the actual extremes of temperature on ships

due to insolation. Light reflecting paints could do much to reduce this effect as in

similar circumstances to those giving a rise of 35°C in a black surface the

corresponding rise on white and aluminium surfaces was only 5.5° to 8.5°C.

6. Combinations of any of the above five circumstances. Unfortunately very little data

on extremes of temperature are available.

7. Heavy weather coupled with any of the above conditions.

Moatsos, I. 2005


In any case the last statement, of the aforementioned, appears to be the most important as

there is evidence that ships structures can withstand the stresses set up by temperature

gradients far in excess of anything quoted above. In the case of bitumen (tar-like substance

which is a direct product of oil refinement) it is usual to load the bitumen at temperatures as

high as 180°C and to heat it for pumping to temperatures in the region of 150°C.

Interestingly none of the casualties, as reported by Hechtman (1956), was associated with

this type of ship. Based on this evidence, items (2) and (3) from the aforementioned list

involved temperature gradients much too small to cause failure themselves although many

ships undoubtedly failed in regions where such conditions are prevalent. It has been

suggested (Miller, 1956) that "thermal shock" might be in part responsible for these

instances but the time scale involved appears too large for this to be the case. Taking all

these effects together it would seem that the worst combination would be very hot internal

liquid coupled with either low sea temperature or low air temperature or both, or the ship

refrigerated internally and subject to bright sunshine. At worst this could lead to a gradient

of the order of 110°C.

As already mentioned if the temperature gradient involves very low temperatures then

brittle fracture may result if the temperature is below the transition temperature for the steel

but the temperature stresses associated with such fractures may be comparatively low,

especially if high tensile stresses exist due to static loading or some other cause. This

emphasises the importance of judicious still water loading. It is possible that when low

temperature conditions are expected, the still water loading can be arranged to place the

parts of the hull girder having tensile stresses into compression. Indeed the possibility of

neutralising the tensile stresses set up by temperature stresses by suitable loading conditions

might be studied for both hot and cold conditions especially in tankers carrying oil at high

temperatures. The thermal stress pattern which may arise in the hull of a tanker can be seen

in the appendix (Fig. 5.1-Fig. 5.3). The stresses are shown with the longitudinal bulkheads

first at the water temperature and then at the temperature of the deck. A number of

interesting points can be made raised from the graphs:

1. The thermal stresses in the main deck and bottom plating for the 10°F

differential are relatively small.2. The maximum tension stresses occur just above the waterline, and the maximum

compression stresses just below the waterline.

Moatsos, I. 2005


3. The maximum tension stresses range from 50 to 75 per cent of those

corresponding to full restraint against thermal strain.

4. In the figures, the maximum tension stresses are developed at the smallest draft,

while stresses in the deck and bottom are not greatly affected by the draft.

5. The effect of having the longitudinal bulkheads of the T-2 tanker at different

temperatures has a small change in the values of the thermal stresses.

According to Hechtman (1956) and all the available published literature on the subject,

ships have suffered severe fractures when the early morning rays of the sun were directed at

the side of the vessel but did not strike the main deck. Thermal stresses for a T-2 tanker

under such conditions of insolation can be seen in the appendix (Fig. 5.3). The maximum

tension stresses occur in the vicinity of the bilge and in the main deck, in each case on the

side of the hull toward the sun. At these two locations they are approximately 25 and 20 per

cent, respectively, of the stresses for full restraint of thermal strain. The appreciable amount

of energy stored in the relatively warmer side shell can be seen.

The important factor in any case is really the probability of the occurrence of adverse

temperature conditions in conjunction with other adverse loadings but when examining the

route that a vessel would take such information would only apply to that particular single

route and it is doubtful if it will ever be wise to design a ship structurally for the

temperature variation on one particular route since the changes in the pattern of world trade

over a ship's lifetime may force many changes in its use.

Concentrating on the determination of the extreme gradients that may occur and estimating

the stresses which will result in particular cases data is required on the extremes of

temperature due to:

1. Changes in sea water temperature

2. Changes in air temperature

3. Maximum differential between positions (a) and (b) at any position

4. Maximum solar radiation

5. Changes in internal temperature of the ship

Moatsos, I. 2005


Meteorological data supplied over a number of years from weather ships or weather stations

can provide sufficient information on items 0), (2) and (3) of the aforementioned list. Solar

radiation is rarely recorded at sea but sufficient data is available for its effects from land

observations for a reasonable inference of its maximum effect in the light of other

meteorological observations. Item (5) can readily be determined for any particular vessel

but a margin of human error should be allowed as is shown by the number of cases where

the temperature of the water for tank cleaning was much above the recommended

temperature.

5.6 Fluctuations in Marine Structural Temperatures

A strong dependency exists between the temperature fluctuation that a ship's structural

components experience during its lifetime and the temperature of the surrounding air and

water and on the hold temperature. The changes in the temperature that occur in the air and

water surrounding the external surfaces of the ship are, to a certain extent, influenced by

such obvious factors as the ship's geographical locality, the season, the particular time of

the day, and the prevailing weather conditions. Alteration in hold temperature conditions, on

the other hand, reflects particular service conditions of the vessel. To bring an example to

this statement, let us consider the cases of a refrigerated ship and a vessel carrying liquid

cargo, such as fuel oil, in the winter. In the case of the refrigerated ship, the temperature of

the structural components can vary from the temperature of the hold to temperatures

approaching those of the outside environment, whereas in the case of the liquid cargo

carrying vessel, the structure's temperature must reflect the cargo temperature and the lower

temperature of the external environment.

When investigating the thermal stress problem, we are mainly concerned with the

temperature of the ship's structure and we are only interested in the temperature of the

surrounding medium only insofar as it helps us to establish the temperatures of the adjacent

structure. It is convenient then to think of the ship's structural components as those with

surfaces exposed to either the cargo or inside air or to an outside environment of water and

air. The structural surfaces that are in contact with the hold medium or the water we assume,

that the temperature at the structure's contact surface is the same as that of the surrounding

medium. We cannot use the same assumptions for surfaces exposed to the external air

environment such as the portion of the vessel that lies above the waterline as these surfaces

Moatsos, I. 2005


are subjected to solar radiation and, as such, develop temperatures higher than that of the

ambient air. Factors influencing temperature differences that can exist at anyone time

between the exposed surfaces and the ambient air are many and include:

1. Insolation: The rate of solar radiation striking and exposed surface.

2. Weather Conditions: Humidity, cloudiness, wind and precipitation.

3. Heat Transfer: The heat transfer characteristics of the exposed surfaces.

Hechtman (1956) provides a good description for the way in which these factors affect the

surface temperature of a ship.

Temperature problems in marine structures have cyclic characteristics which can be easily

made evident when one considers the effects of solar radiation. Let us consider a case where

a vessel is moored in a particular location for a one year period, during which the

temperature of the water is always constant and the atmospheric conditions are such that

they never influence the rate of radiation striking a surface. Assuming that the vessel can be

oriented to such a fashion as to always permit the vessel's surfaces to have the same

orientation with respect to the sun during any given daylight hour, permits us to eliminate

the influence of diurnal variation of insolation and under such assumed conditions, the

surface temperature of each part of the vessel's structure exposed to the sun will change

during each 24 hour period. The extent to which the structure's surface temperatures would

change each day could be somewhat similar to the figure shown in the appendix (Fig. 5.4).

In this hypothetical case, if the vessel was subjected to the described conditions for a period

of 20 years, it would experience 7300 temperature cycles and an equivalent number of

thermal stress and strain cycles. In a sense then, the vessel's structural material will be

subjected to cyclic phenomena similar to those encountered in a thermal fatigue test. In an

actual ship though the daily temperature cycles resulting from the solar condition would not

be the same as in our hypothesis as service conditions and climatic and seasonal changes

would influence the day-to-day temperature fluctuations. Under such conditions, the

vessel's structural material would be subjected to temperature conditions that could be

described as a random, thermal-cycle fatigue phenomenon.

Whether or not the cyclic character of temperature fluctuation is of importance in

determining the structural integrity of a ship is not clearly known and this is quite evident

Moatsos, I. zoos


from all the relevant published literature. It seems reasonable to assume that the cyclic

nature of the temperature variations and the resulting thermal stress conditions should alter

the materials, and thus the ship structural characteristics. After careful examination of the

published literature at the present time there is not sufficient available materials data to

judge the significance of the cyclic temperature condition encountered during a ship's

normal lifetime. In addition to this the method of analysis for the steady-state temperature

conditions is yet to be mastered to such extent as to feel comfortable to proceed with the

exceedingly more complex cyclic temperature problems. As a consequence, the approach

used by the author and all analysis carried out has ignored the cyclic character of the

temperature problem as there is no alternative but to wait for further developments in the

state of the art.

5.7 Temperature Differentials

As mentioned in the previous section, our main concern with the surface temperatures of a

ship's structure is not with the temperature per se but more with the temperature differences

that can arise between different parts of the structure. If we assume a situation where the

temperature of every single structural component of a ship increases uniformly during a

specified time interval and by assuming that a temperature gradient did not exist at any time

in any portion of the ship's structure, it would be necessary to merely observe an increase in

the ship's dimension in all directions and to compute these changes in dimension by using

the familiar coefficient of thermal expansion for the material. Unfortunately uniform

temperature distribution does not occur in marine structures.

As a matter of convenience throughout this research the author has considered only those

temperature differences that exist at a specific time and under certain environmental and

services conditions treating each temperature problem as if it was occurring for the first

time and ignoring past or future temperature conditions. The only manner in which the

element of time-dependency will enter into the discussion will be on a later stage when the

thermal stress calculation will be combined with ultimate strength formulation to be used in

time-dependent reliability analysis.

Moatsos,l. 2005


A number of cases exist which give rise to significant temperature differentials and which

contribute appreciably to the deformational characteristics and structural integrity of the

ship:

a) Waterline: Significant temperature differences exist on the exterior of

surfaces of the hull's side plating. This vertical temperature gradient is a

consequence of the plating above the water being subjected to ambient air

temperature and solar radiation while the plating below the waterline reflects

the relatively constant temperature of the surrounding water. Under certain

circumstances, two different situations can arise where, in one case, the

temperatures of the exposed plating above the waterline can be above that of

the plating below (Fig 5.5), while in the other, the exact reverse can occur

(Fig 5.6). In the first case the temperatures shown are the hull plate

temperature changes (the increase in temperature achieved at each

instrumented point above the waterline during the interval between an early

morning reference hour and a later daylight hour) as measured on the surface

of the plating during one day. In the second case the temperature distribution

merely represents the difference in temperature between the ambient air and

the water. It can be surmised that this represents the condition at some point

during the night, thereby excluding the effects of insolation and permitting

the use of the ambient air temperature to denote the structure's surface

temperature. We can then conclude that if the temperature difference of -

10°F (5.55°C)represents the maximum temperature change during a specific

time interval, the reference hour must be taken as that hour of the day when

the temperature of the structure's surfaces exposed to air was the same as the

water temperature.

b) Differences in surface finish: Abrupt temperature gradients can also occur in

the portion of the hull above the waterline as a result of different types of

surface finish. Such conditions are directly attributed to the surfaces' solar

radiation-absorption characteristics. Examples of the effect of surface finish

and colouring can be found in the appendix (Fig 5.7). The importance of the

colouring as it influences the temperature of certain portions of a ship's

surface when subjected to a particular intensity of solar radiation can also be

found in the appendix. (Fig 5.8) where it can be noticed that, at the dividing

line between those portions of the ship's surface painted black and those

Moatsos, l. 2005


painted white, a surface temperature change of 15°F (8.33°C) occurs over a

distance of only 3ft (O.9144m).

c) Non-uniform exposure to solar radiation: Temperature differences also arise

when the exposed surfaces of the ship do not receive the same amount of

insolation which is partially dependent on the orientation of the surface with

respect to the sun (Hechtman, 1956). Under such conditions one would

expect a considerable difference in surface temperature to exist between the

hull plating on the port and starboard side above the waterline during early

times of the day when the sun is rising, say, on the port side as well as a

temperature difference between the portion of the decking on the port side

and that on the starboard. The condition of thermal symmetry shown in (Fig

5.6) is only possible when the sun is immediately overhead.

d) Difference between hold and external temperatures: Although we have

limited our discussion of temperature differences to those occurring as a

result of external phenomena, it is quite apparent that for ships that carry

liquid or refrigerated cargo, the temperature of the internal environment can

have a very pronounced effect on the temperature throughout the transverse

section of the ship. It is most convenient to describe temperature gradients

that result from differences in external and internal environment

temperatures by a means of a sketch (Fig 5.9) Looking at a comer where the

plate ABC is the deck, the plate ADE, the side of the hull, and the plate FGHI

the bulkhead, we assume that the temperature gradient is uniform in the X-

direction and through any plate thickness. The deck and hull plate

temperatures shown represent the increase in temperature during a particular

interval of time above the inside temperature of the ship. It is noticeable that

the temperature gradient in plate FGHI can then vary in both the Y- and Z-

directions thereby creating a two-dimensional thermal stress problem. Kayan

& Gates (1958) propose an interesting analytical approach for describing

such temperature conditions by using a "simple fin" treatment in which the

temperature gradients for any type of extended surface projections (fins)

exposed to different temperatures can be found by direct analysis, a

numerical method or by an electrical analogy. This procedure although it is

applied to the steel frame of a building, would be equally applicable to the

framing members of a ship.

Moatsos, I. 2005


e) Across plate thickness: Temperature can vary from point to point within and

on the boundaries of structural component. In the case of a flat plate where

one surface is exposed to an environment at one temperature and the other at

a different temperature, then obviously a temperature difference must exist

through the thickness of the plate. It is debatable whether the temperature

gradient through the thickness of a plate is of practical significance and

dependant on many factors such as the temperature difference between the

two surfaces, the plate thickness, the thermal conductivity of the plate

material and the surface heat transfer coefficients on both sides of the plate,

assuming that the plate and the surroundings have attained a condition of

steady-state thermal equilibrium. In reality, however, the plate temperature is

dependent on time which becomes quite self evident when it is recognised

that a plate can store heat and can emit and absorb heat (by radiation, by

conduction to internal structural components and by conduction or

convection to the internal air or cargo). For the purposes of this study we are

mostly interested in the maximum temperature difference that can exist at

any given time across the plate'S thickness since this would be the condition

that would give rise to the most severe thermal deformations. In any case, it

is always necessary to know of a significant temperature difference actually

does exist across the plate thickness. If it does exist, it then becomes

necessary to describe the thermal gradient across the plate's thickness.

5.8 Calculation of Temperature Gradients

Having determined the range of temperature possible it will then be necessary to estimate

the temperature gradients which are likely to occur in a particular ship. With structure,

loading and operating conditions of ships being so variable significant work carried out in

the area of heat transfer is not directly applicable. In particular, design details such as

bracket connections on longitudinals, hatch comers, etc vary so greatly that an immense

effort would be required to study particular cases theoretically. For this type of problem

model tests under controlled temperature conditions are likely to yield much quicker and

more accurate results. The temperature gradients which will arise away from structural

details can be estimated with sufficient accuracy as a result of full scale tests as reported by

Meriam et al. (1958) and Ossowski (1960). None of the test data available were obtained on

Moatsos, 1.2005


loaded dry cargo ships and possible variations are so large that it would be very expensive

to investigate the effects fully. The cargo will in nearly all cases provide an increased

thermal capacity and will reduce the effects of sudden changes in temperature so that an

empty ship probably constitutes the worst case.

5.9 Calculation of Temperature Stresses

As described in the literature review for this subject in Chapter 3 of this thesis, a number of

authors have suggested methodology for the calculation of the longitudinal stresses in the

hull girder resulting from two dimensional temperature gradients and all the methods

produce similar results with Jasper's (1956) statement of the problem, based on Timoshenko

(1934), as recommended by SSC Reports No. 95 by Hechtman (1961) and No. 240 by

Lewis et al. (1973), is the clearest and most applicable. Before the magnitudes of the

thermal stresses are formulated in detail, one should consider how thermal strains are

related to thermal stresses.

5.9.1 Elementary Thermal Stress Relationships

Let us consider a small element of material (Fig 5.10) that experiences an increase in

temperature. If it can be assumed that the entire element attains a uniform temperature of Tf

during a given time interval and that the element is free to expand, then the thermal strain

developed in any direction is:

e, =a,T (5.1)

where et is the thermal strain, Q1 the coefficient of thermal expansion which is a weak

function of the temperature and the direction chosen for measuring e, and T the temperature

change.

Let us now assume that the element is also subjected to hydrostatic pressure of such

intensity as to partially cancel out the thermal expansion:

(5.2)

Moatsos, I. 2005


Since our study is limited to linear-elastic isotropic materials then for Young's Modulus:

(5.3)

and the strain Co in any direction resulting from the stresses 0"0 is:

(5.4)

where Vt is the Poisson's ratio. The net strain resulting from thermal expansion and

compression owing to the hydrostatic pressure is thus the algebraic sum of the individual

strains:

e=et =£0 = 0"0 (1-2vt)+atTE,

(5.5)

If the hydrostatic pressure, which may now be thought of as a restraint on the thermal

expansion, is sufficient to cancel fully the free-expansion thermal strain (possible only with

an infinitely rigid restraint with zero clearances), then:

e= 0= 0"0 (1- 2v )+a TEt',(5.6)

or

-a,TE,0"0 =

1-2v t

(5.7)

If the concept of using equal stresses in three dimensions as a means of restraint is

abandoned, and if it is assumed that the degree of restraint that occurs in the X-, Y-, or Z-

directions differs, then following the same procedure as was used to derive Eq. (5.5), it is

possible to derive the following equations for total strain for an isotropic material:

Moatsos, I. 2005


Cx= C~ + C, = _1_[(0" IX- V, (0" ty + O",J)]+ a,T

E,

cy =C~+C, = ~ [(O"ty-VI(O"IX+O"/Z))]+a,TI (5.S)

rxv.YZ.Urxy,)7.,U = IisI

On the other hand, it is possible to express the thermal stresses in terms of strain:

O"IX=k1e+k2cX-k3a; =k,e+k2cy -k3O"/Z=k1e+k2cz -k3

(5.9)

where:

k = vrEr1 (1+vIXl-2v,)

k -_5_2-1+v I

k _ 2aE,T3- 1-2v,

e=e, +cy +cz

(5.10)

For an unstressed bar, a detailed description can be found in the appendix of this chapter.

5.9.2 Thermal Stresses on a BoxGirder

Before the application of thermal stress theory described in previous sections can be applied

to an idealized girder of uniform cross section throughout its length with connections

between the sides of the box assumed hinged, as it can be seen in the appendix (Fig 5.12), ,

the number of assumptions that were made have to be clearly stated:

Moatsos, I. 2005


• The plating in ships is sufficiently thin so that usually no significant temperature

difference can exist across the plate thickness and most theoretical solutions for

thermal stresses in plates assume uniform temperature across the thickness

• The position, when it comes to details of the girder, is not so good and little is

known about the effect of temperature gradients in a way of positions likely to give

rise to stress concentrations.• The usual elementary theory of bending of beams is assumed to be applicable. Thus

in the initial development it is assumed that there are no restraints which would

prevent deformation in the transverse planes and that O'y=OZ=O. Later it will be

shown that if such restraints were fully effective in a thin-walled box beam, for

example, by providing closely spaced rigid diaphragms, all the stresses throughout

the beam will be modified in the same ratio. The actual stress variations in a box

beam should lie somewhere between these two extreme assumptions of full and zero

transverse restraint.• The change in temperature distribution is identical in every transverse cross section

of the beam.• There are no external moments or forces acting on the beam.

• St. Venant's principle applies.

To determine the stress distribution in a transverse section of an idealized ship girder, one

can reach the conclusion from the assumptions that the stress distribution is the same at

every transverse section sufficiently distant from the ends of the beam. As required by

equilibrium the net moment, the total longitudinal force and the total transverse shear force

in any direction at any transverse section must be zero. With the assumption that the girder

acts as if it were made up of separate longitudinal fibres fitted together in the form of the

ship girder these are initially allowed to expand freely due to temperature changes. Stress

fields are then imposed so as to satisfy the requirements of continuity, geometry,

equilibrium and the boundary conditions imposed. By choosing the origin of the coordinates

so that the Oy and Oz axes coincide with the principal centroidal axes of inertia, for beams

constructed of more than one material initially a set of stresses 0'1 is defined preventing all

longitudinal fibres of the beam from thermal expansion.

(5.11)

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Both E and a can vary over the cross section, where a is the coefficient of thermal

expansion. Then a constant stress 0"2 is added which will make the total longitudinal force

on the section zero. Now Oi must vary in proportion to E in order to equalize strain in all

fibres:

E2 JEAdA- JaAEATAdA=O=>O"n =E2EL

JaAEATAdA=> O"n = EL JEAdA

(5.12)

A set of stresses 0"3 and 0"4, corresponding to pure bending in the Xy and Xz planes

respectively (the x axis being longitudinal), is added to the stresses (YJ and 0"2 so that the net

bending moment at the section equals zero. One can achieve this by choosing the Oy and o,

axes to coincide with the principal centroidal axes of inertia but if E is allowed to vary then

with the principal area of El. So initially for a homogeneous beam by taking moments about

the o, axis:

(5.13)

This expression is obtained by taking moments about the oz axis, therefore:

(5.14)

from,

(5.15)

And similarly,

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(5.16)

from,

(5.17)

Since the Oy and Oz axes are chosen to coincide with the principal centroidal axes of inertia,

(5.18)

(5.19)

(5.20)

Now for a composite beam in pure bending,

(5.21)

Also we locate the axes so that bending in the Yx and Zx axes is uncoupled so that the strain is

proportional to y or z respectively,

JEydA = JEzdA = JEyzdA = 0 (5.22)

This determines the principal centroidal axis of an area comprised of area elements EdA,

which have the coordinates y, z of dA. So,

(5.23)

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(5.24)

Where kJ and k2 are constants.

Ey ICF3 = I aETydAEidA

(5.25)

Ez ICF4 = I 2 aETzdA

Ez dA(5.26)

The resultant stress distribution (which is the sum of the four CFcomponents) is the desired

solution inasmuch as it satisfies the requirements of equilibrium, continuity, beam theory

and the boundary conditions, except near the ends of the beam (Fig 5.13). By St. Venant's

principle the solution will be valid at sections distant from the ends of the beam, even

though the boundary conditions are not completely satisfied at the ends of the beam.

(5.27)

IaETdA Ey E:(J' = -aET +E J + J JaETydA + J JaETzdAEdA EidA Ez2dA

(5.28)

This can be also written as:

kI kvI kZICF = -aET +- aETdA + -(I ') aETydA +r;T aETzdAA£ 0. e ,lo\, J ... £

(5.29)

where,

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..

(5.30)

With E, an arbitrary constant which in our case is the Young's Modulus of mild steel. Eq.

(5.19) provides the stress distribution for any given change T in temperature distribution in a

non homogeneous beam but up to this point we have assumed that no transverse restraint

has been applied on the beam. With the existence of transverse bulkheads in a ship structure

providing such a transverse restraint, which to some extent will prevent the free transverse

expansion of the sections during a temperature change, those effects should also be taken

into account. To achieve this some additional assumptions have to be made:

• The walls of the box beam are thin so that there are no stresses normal to the

thickness of the wall.

• The cross-sectional shape and dimensions are preserved by closely spaced,

imaginary diaphragms, which are rigid in the plane of the diaphragm and free to

warp out of their plane.

• The diaphragms are insulated from the box beam and the temperature of the

diaphragms remains constant while the walls of the beam are subjected to

temperature changes.

To determine again the stresses i.e. eX=O, the stress strain temperature relationships are,

(5.31)

(5.32)

(5.33)

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For horizontal surfaces (parallel to the xz p1ane, such as the top deck) 0.=0 as it occurs from

the second assumption, therefore from Eq. (5.31) to Eq. (5.33) by equating Ex to 0. it is

found that,

._

(5.34)

Using this and the first assumption made (that ay=O) Eq. (5.31) gives,

aET(I-V)

And with similarly the desired normal stresses a] in the axial direction and the peripheral

normal stresses a8 parallel to the yz plane are given by the expression derived above:

aET(I-V)

(5.35)

By substituting the value of a], which includes full effective lateral restraint, in p1ace of the

value previously used we obtain the final relationship for s since none of the remainder of

the theory used is affected by the addition of the restraint.

aET k J ky J k: Ja= (_ )+- aETdA+-( -)- aETydA+~ aETzdA1 V A£ 10: £ \IOY )e

(5.36)

It is noticed that the stress changes induced by temperature changes are greater when a

transverse restraint is acting than would otherwise be the case. If, for example Poisson's

ratio v=l/3 is used then the stress variations will be increased by 50 percent. The actual

stress in a box beam would be expected to lie somewhere between those obtained for the

assumption of zero restraint and full transverse restraint.

As suggested by Lewis et al. (1973), apart from the average diurnal change in air

temperature a number of other parameters, as already discussed, had to be taken into

account. Deck p1ating would be subjected to this temperature change plus the change due to

inso1ation (the absorption of radiant heat). The temperature change due to insolation

Moatsos, I. 2005


depends on cloud cover and the colour of the deck. As an approximation according to

Taggart (1980) the appendix (Table 5.3) shows maximum differences between air and deck

(sun overhead. unshaded) for different colour of the deck.

It was assumed in our case that the deck colour in all FPSOs was dark grey. The prediction

of average thermal stresses and expected maxima requires also that the frequency of

occurrence of different conditions of sun exposure be determined. The assumption of the

vessel operating constantly in the North Sea simplified this and monthly cloud cover data

was used averaging from 1978 to 1998 and specifically on the dates of extreme temperature

changes. Initially a simplified distribution of L1T is assumed with the temperature remaining

constant over the deck and the sides down to the water line and L1t=O elsewhere (below WL)

(Fig 5.14) and then for an asymmetrical distribution of L1T with the temperature varying

accordingly (Fig 5.15). Longitudinals are assumed to have the same L1T as the plating.

which they support. Longitudinal bulkheads and associated longitudinals are assumed to

have L1t decreasing linearly from the deck L1t at top to L1t=O at the assumed level of oil inside

the tanks. The vessel is also assumed to be initially at a state of zero stress and while on the

stocks. when the final welds in the cross-section were made. the temperature of the upper

deck exposed structure would be lower than the more sheltered lower parts of the hull.

5.10 Experimental Data on Temperature Stresses & Full Scale Measurements

As already mentioned in Chapter 3, the earliest data on temperature stresses were produced

as a by-product of full scale tests on ships to determine the behaviour of the hull girder

under various loading conditions. In a review of the data obtained from the early tests. as

given by Hechtman (1956) is shown that stresses of the order of 76N/mm2 (5tonlin

2)were

associated with a temp of 22.78°C (73°F). Generally speaking the instrumentation on these

tests was not elaborate enough to enable rigorous comparison of theory and experiment as

far as temperature effects were concerned. Corlett (1950) carried out tests on a box shaped

model made of steel with an aluminium superstructure under controlled temperature

conditions with good confirmation of the two dimensional theory obtained. In the 1960s a

very extensive investigation was carried out on behalf of the SNAME S.l 0 panel as reported

by Meriam et al. (1958). In this case the whole instrumentation was designed especially for

temperature stress measurement on a laid up cargo ship subject to large diurnal temperature

variations. The maximum deck temperature during the test was 29.5°C and the maximum

Moatsos, l. 2005


stress recorded was of the order of 60.81N/mm2 (4tonlin2). The ship was empty at the time

of the test and the temperature gradient through the plating was negligible under these

conditions. The extremely good agreement between the measured stresses and those

calculated using Jasper's (1956) method indicate that reliable results can be expected from

purely theoretical investigations into the effects of heating or cooling the internal structure

of the hull. This has also been confirmed by tests performed in the 1960s by the British Ship

Research Association (BSRA) on a tanker loaded with oil at 95°C when the sea and air

temperatures were of the order of 5°C. In this case since only the centre tanks and a few

wing tanks contained the hot oil there was a considerable three dimensional gradient

imposed on the hull but the two dimensional theory neglecting transverse restraint gave very

good agreement with the measured stresses. The highest value measured was 147,44N/mm2

(9.7tonlin2) towards the base of the longitudinal bulkhead but it was believed that slightly

higher stresses occurred in the bottom centre girder. The maximum stress in the outer shell

was 59.72N/mm2 (3.9tonlin2). In this case the longitudinal bulkhead was transversely

framed so that the plating buckled between the frames and thus helped to relieve the loads

imposed on the remainder of the hull. More severe loading would be expected with a

longitudinally framed bulkhead in which case higher stresses in the hull would be expected.

Unfortunately there are few experimental results that can be used as an aid to engineering

judgement to determine whether or not the thermal gradients that can exist across a ship's

plating thickness are of any practical importance. Tests in Meriam, Lyman, Steidel &

Brown (1958) reveal that the maximum temperature difference measured across any plate

thickness was only 0.74°C (1-113 OF).This program, however, only involved measurements

of temperature at various points on both sides of the plating in an empty Victory-Class ship

where the environmental temperature data available showed that the maximum air

temperature differential was 8.33°C (l5°F) between the air in the upper 'tween deck and the

air in the lower hold. This is a rather mild temperature condition which does not at all

approach the more adverse temperature states already discussed.

The ultimate objective of an experimental investigation of thermal effects on a ship's

structure is to acquire strain data so that it may be possible to ascertain the validity of the

thermo-elastic theories used to compute thermal stresses and deformations. To accomplish

this objective, experimental programs must at the same time acquire data describing the

temperature distribution as well as the temperature changes that occur in the ship's structure

Moatsos, I. 2005


during a given period of time. Furthermore, if such temperature data are to be meaningful, it

must completely define a reference time and temperature and all the possible conditions that

could influence the ship structure's temperature state. Other experimental programs may be

undertaken wherein only the temperature data are acquired and no strain measurements are

taken. Knowing the temperature state of a ship structure at any given time, however, merely

provides data that can be used to compute a change in the stress and deformation state.

The majority of the ship temperature investigations reported in the literature give

temperature data measured for a very restricted set of environmental conditions. This type

of experimental information has been thoroughly discussed in the published literature. In the

past, investigations involving thermal stresses in ship structures have, for the most part,

been limited to taking an assumed or experimentally acquired temperature condition and

then using this temperature information to compute the thermal stress. Other experimental

studies that have been reported (Meriam et al., 1958), on the other hand, represent a well

organised investigation that makes a concerted effort to acquire experimentally a

quantitative measure of the thermal strain induced in a ship. When comparing theoretical

results with experimental data available it is worthwhile to discuss a few of the interesting

points that arise from such an exercise.

As it can be seen in Appendix 5, (Fig. 5.16 & Fig. 5.17) we can observe the temperature

changes, the measured, longitudinal thermal stress changes, and the computed, thermal-

stress change for two test times (1335 PDT and 1810 PDT) according to data available in

Meriam et al. (1958). The computed thermal stresses were acquired by using the approach

& equations described in this chapter of the thesis, with a and E assumed constant. It is

evident from these figures (Fig. 5.16 & Fig 5.17) that an excellent correlation exists

between the stresses defined by the measured strains and those computed using the

approach selected by the author. We can then safely conclude, as it can also be found in

Meriam et al. (1958), that an approach, based on a beam equation neglecting the transverse

strains and based on the assumption that the temperature distribution in the longitudinal

direction is uniform, is adequate for the particular test section used in the investigation. We

must pay particular attention though to the fact that the test section used was located in a

portion of the ship where the transverse stiffness resulting from bulkheads was minimum

and the temperature and strain gradients in the longitudinal direction were small.

Moatsos, I. 2005


As described again in the investigation by Meriam et al. (1958), evidence of both local plate

bending and buckling was found. By taking strain measurements on both the inside and the

outside surface of the plate above the waterline, a location was found where the plates'

bending stress reached a magnitude of 82.737 N/mm2 (12 Kpsi), occurring on an early

morning on the starboard side with the sun rising on the same side. Evidence of local plate

buckling was also found during the same test period.

5.11 Metocean Conditions & Temperature Statistics North Sea

The North Sea experiences a relatively wide range of air temperatures that vary within

season, as it can be seen from the appendix (Table 4.1) according to the IMarEST Technical

Affairs Committee (2004). Visibility is generally reduced by occurrences of fog resulting

from high humidity caused by warm air over cooler seas. Fog is more common during

winter than summer, and is more likely to occur close to the shore. The variation in sea

surface temperature is greatest in the summer, as it can be seen again in the appendix (Table

4.2), due to greater heat transfer in the southern latitudes of the North Sea. Stratification of

the water column occurs in the Central and Northern North Sea, but in the Southern North

Sea due to tidal mixing.

In the absence of available recorded air temperature data from FPSOs in the North Sea, data

had to be obtained from a different source (Fair Isle Weather Station, 2005). Fair Isle is the

most southerly island of the Shetland group (the northernmost islands of the British Isles). It

lays approximately 25 kilometres South South West of the Shetland mainland (Fig 5.18),

and approximately the same distance northeast of North Ronaldsay (the most northerly of

the Orkney Islands). To most people in the UK Fair Isle is a name known from the BBC R4

Shipping Forecasts. Since it is in the North Sea its climate accurately represents the

conditions that exist in the area throughout the year. Air temperatures and cloud cover data

for the period 1978 to 1998 was used and since the diurnal variation of temperature was

required the daily average maximum and minimum temperatures recorded were used. From

all the years a seasonal average and seasonal extreme values were selected to provide an

extreme and average model of the climatological conditions experienced in that area and

that would be very close to the conditions experienced by installations in the North Sea. The

assumption was made that there is no significant difference between air temperatures

recorded on Fair Isle and air temperatures recorded on the actual installations. This can be

Moatsos, I. 2005


said to be very close to the truth since Fair Isle is geographically situated to the North of the

FPSO locations and measurements taken in that area (even though they are taken over land),

would represent the worst possible conditions that an FPSO could experience. The same

procedure was followed for the cloud cover data requiring again obtaining average and

extreme values. In the appendix in (Fig.5.19) the average temperature for each of the

months of the year for the 1978 to 1998 period used in the analysis can be found in

graphical format. Also in the appendix (Fig 5.20) the figure shows an example of the air

temperature in Fair Isle for the year 1989 (one of the years that an extreme seasonal change

in temperature was recorded) from which it can be seen that the months during which

extreme temperature are usually recorded are May until late August-September (the spring

and fall months exhibiting the largest diurnal differences) and that differences during these

months can be as high as 18.37°C (the largest temperature difference recorded for the time

period analysed). Hence five temperatures were selected representing five distinct cases that

can be encountered:

I. I I.7°C: The average seasonal diurnal change in temperature

2. 16.01°C: The extreme summer diurnal change in temperature based on monthly

averages for the time period analysed.3. 16.26°C: The extreme winter diurnal change 10 temperature based on monthly

averages for the time period analysed.

4. 17.2IoC: The extreme fall diurnal change in temperature based on monthly averages

for the time period analysed.5. 18.37°C: The extreme spring diurnal change in temperature based on monthly

averages for the time period analysed.

For each of the years of extreme temperature changes the cloud cover can also be seen in

the appendix, (Fig. 5.21). Cloud cover data enables the procedure to be fully implemented

without any assumption needing to be made for the area and thus obtain accurate results for

the specific area that the FPSO vessels are operating.

5.12 Time-Dependency in Temperature Effects

The thermal problems dealt in this study, for the most part, are limited to time-independent

temperature conditions involving those temperature conditions that exist at a specific instant

Moatsos, I. 2005


of time, and the rate at which the temperature changed before and after that instant of time

was not incorporated in the analysis procedure. Stating the same condition in another way,

the discussion has not dealt with the transience of the temperature conditions, but has

assumed that the temperature distribution at the instant of interest represents a steady-state,

thermal equilibrium condition. Thus, the temperature terms are not stated as functions of

time, and the equations derived for thermal strain, stresses and deflections are also

independent of time.

This is really not the case for any real structure, and it is certainly not true for a ship's

structure as in ships, the ever-changing environmental conditions themselves deny the

existence of a truly time-independent temperature state. In addition to this any structural

component will store, radiate and conduct heat to other components, convect or conduct

heat to or receive heat from the external and internal media. There are, however, two

reasons which serve to justify the adoption of these restrictions. One is that for the design

and analysis of marine structures, we usually seek the maximum values of strain, stress and

deflection, resulting from isolated thermal conditions. The second reason lies in the fact for

ship structures there is little or no information to which we can base our study when

investigating whether or not transient temperature conditions are of practical importance to

a ship's structure. It is not likely that the rate of change of stress resulting from temperature

transients will be enough to alter the static properties of the structure.

5.13 Discussion-Results

5.13.1 Results Obtained

By following the theory and the procedure already described in Section (5.9) and Section

(5.10) of this chapter and the recommendation of the sse suggested procedure as stated in

Lewis et al. (1973), the temperature change was calculated for all 3 TankerlFPSO structural

design generating thermal stresses occurring from extreme and average diurnal changes in

temperature for the North Sea. The stresses were then combined with the ultimate strength

data obtained to produce the ultimate strength of each stiffened panel but also an overall

ultimate strength of the hull girder for the two FPSOffanker structures analysed. The full

details of the theory behind the calculation of the US will are described in (Chapter 6) and

the overall results and their significance are discussed again in (Chapter 10) in the

concluding part of this thesis.

Moatsos, I. 2005


Jasper's theory has a number of assumptions that require attention and are worthy of some

discussion. Although the theory neglects the effects of transverse restraint on the

longitudinal stresses, good agreement has been shown between theoretical calculations and

experimental results on both model and full scale. Away from transverse bulkheads it

appears the transverse restraint is small and the theory is satisfactory for the longitudinal

strength problem.

An interesting point arises in all theoretical approaches suggested that solutions for the

thermal stress problems for holes in plates under various boundary conditions all indicate

stress concentrations of the same order as under tensile loading conditions so that the two

effects may well be superimposed in cases where there is a temperature gradient over the

stress raiser as well as tensile stresses in operation. This would explain the cracks that have

been observed around piping holes and other stress raisers in refrigerated ships and

emphasises the importance of detail design when the detail itself is subject to a temperature

gradient.

The results of the analysis for 1 FPSO as a sample can be found, for each of the cases

examined in Graphs the Appendix. Starting with (Fig. 5.22) showing the average seasonal

diurnal thermal stresses for each part of the FPSO structure, plotted against the height of the

structure, (Fig. 5.23) for the extreme winter, (Fig. 5.24) for the extreme fall, (Fig. 5.25) for

the extreme spring and (Fig. 5.26) for the extreme spring, all demonstrating the same trend

as illustrated in (Fig. 5.15) for an assumed asymmetrical temperature distribution.

The overall effect on the US of the stiffened plate elements for each part of the FPSO

structure plotted against the height of the structure can be found also in the appendix

starting with (Fig. 5.27) showing the US variation on the outer shell of the structure due to

diurnal thermal stresses for all scenarios examined, (Fig. 5.28) for the inner shell and (Fig.

5.29) for the centerline. Again the effect of diurnal temperature changes can be seen

reducing the US in all of the structural elements.

The overall effect of the diurnal temperature change on the US according to all the scenarios

examined can be found in tabular form in the appendix starting with (Table 5.4) showing

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the calculation for US for the entire hull girder with no corrosion effects and with no effect

of thermal stresses, (Table 5.5) the calculation of US for the entire hull girder with no

corrosion effects for the average seasonal diurnal thermal stresses, (Table 5.6) for the

extreme winter scenario, (Table 5.7) for the extreme fall scenario and (Table 5.8) for the

extreme spring scenario again with no corrosion effects.

The preliminary analysis of the FPSO structure indicated a significant effect. Hogging

ultimate strength change results compared to results that did not include temperature effects

produced a change ranging from 2.6% to 5.1% for the temperature changes examined with

the corresponding change for the average diurnal overall change in temperature found to be

2.6%. In the case of sagging ultimate strength change the results obtained were of the

magnitude expected showing a 41% reduction in ultimate strength during sagging in the

"worst case scenario" analysed. The sagging analysis produced a change ranging from

24.3% to 40.8% for the temperature changes examined with the corresponding change for

the average diurnal overall change in temperature found to be 24.3%. Another reason

between the differences would be the fact that the deck is more prone to buckling than the

bottom. Any assumptions used for the residual stresses in the structure can be found in

Chapter 6 where the formulation used for analysing the Ultimate strength of the structure is

described in detail.

The next step in our study would be to incorporate these results in a Reliability Analysis

performed on the structures in order to get an initial structural reliability estimate for the

design but in order for us to do so we also have to explore the best ways of modelling all the

other physical phenomena that will enable us to formulate all the related variables in our

limit state equation. The next chapters will be devoted to doing so in detail starting with the

next chapter, (Chapter 6) examining the Ultimate Strength of the structures and thus

providing the resistance part of the limit state along with (Chapter 7) describing Corrosion

modelling and this chapter, (Chapter 5) for the thermal stresses.

5.13.2 Proposal on Experimental Procedures

Any concerted effort to include the effect of temperature in the design of ship structures

must begin with the acquisition of temperature data from adequately instrumented ships

over a variety of conditions. The overall research program must include the development of

Moatsos, I. 2005


methods of analysis for thermal stress and thermal buckling that will be particularly suitable

for ship structures. Before such a development can take place, however, it is necessary to

acquire experimentally a sufficient quantity of ship structure temperature data to clearly

identify typical temperature histories. These temperature histories must not only define the

maximum changes in temperature that can occur for a given set of environmental and cargo

conditions but must also adequately describe the cyclic character of the temperature and the

rate at which the temperature changes.

For a structure as large and complex as a ship, this represents an ambitious undertaking

even if the ultimate goal is to acquire only exemplary temperature data. It becomes feasible

and utilitarian if the overall experimental program is well planned so that the end product

can be achieved with a minimum expenditure or time and money and yet guarantee that the

temperature data so acquired do indeed encompass all the conditions that can yield the most

adverse temperature states. The selection of the ship to be instrumented is simultaneously

the first and most important decision that will confront the planner of such a study as a ship

selected from an old fleet will have the advantage of being readily available for continuous,

unhindered experimentation but at the same time has the disadvantage of being

representative of materials, structural configurations and service conditions of a past era.

Such disadvantages would not exist in the case of a newly commissioned ship where

problems would result from conflicts between service and experimental requirements. The

second most important decision that will confront the planner of such a study is the

selection of the location of the temperature measuring devices. The number of points to be

instrumented on the ship's structure must be such as to provide a conclusive picture of the

transverse temperature gradients existing in the hull and the top and 'tween decks at several

typical transverse sections (at bulkheads and between bulkheads), as well as the longitudinal

temperature gradients. In addition, thermocouples should be located on internal structures so

that two-dimensional and three-dimensional temperature gradients could be defined.

The temperature data so acquired would serve as a guide, not only for establishing the

research programs to develop a method for analysis for thermal stresses and thermal

buckling in ship structures, but also for developing temperature equations to describe

transient thermal conditions. With the development of the various methods of analysis,

there arises the necessity of proving the correctness of the theories. Thus, in selecting the

ship and temperature instrumentation, the planners must also take into account the fact that

Moatsos, I. 2005

Chapter S. Thermal Stress 171

the ship must eventually be instrumented with strain gauges. On one hand, the

measurements of strain must distinguish the thermal strains from the strains resulting from

other load conditions so as to permit a check on the validity of theories developed for

thermal analysis. On the other hand, such strain measurements must also reflect the

composite strain picture, for the stresses and deformations resulting from temperature effect

are of consequence in ship structures only when they are superimposed on stresses and

deformations resulting from other load conditions.

Since it is quite evident that additional research programs might be undertaken in the future

to measure thermal strains in ship structures, it would be of practical use to future readers of

this thesis to discuss the experimental problem of measuring the strains and stresses in a

structure subjected simultaneously to external loads and thermally induced loads and

suggest the best methodology for approaching such a complex issue. All approaches

attempting to formulate the thermal stresses on marine structures treat the thermal stresses

and deformations as separate and independent of all the other sources of stresses and strains.

The approaches assume that what has happened to the structure at any time in its past and

the temperature-independent loads existing on the structure do not influence the thermal

stress and strain state. However, it is widely accepted that any point on a ship structure

where a thermal strain might be measured, will quite likely be in a state of strain as a result

of external loads and as a result of fabrication. Therefore, the strain data acquired from a

ship instrumented with strain gages reflect the change in strain resulting from the change in

the structure's temperature, but also from the changes on other load conditions. No specific

published research has been devoted to this problem specifically for ship structures and the

most suitable approach has been reported by Levy (1954) in which a perfectly general

technique for judiciously and correctly locating the strain gages.

Let us consider a structure with a temperature gradient subjected to an externally applied

load of unknown magnitude. If the structure is instrumented beforehand with temperature

compensated strain gages, the measured strains will convey the deformation resulting from

the thermal as well as from the external loads. To separate the thermal effect we can use

Gauss formulas for numerical integration to strategically locate the strain gages so as to

permit a separate computation of the external loads. Consider a beam (Fig. 5.30) with a

temperature gradient in the Y-direction only. If the beam is subjected to the axial force Nx,

then the combined stress distribution will be as shown in (Fig. 5.31). If the total stress

Moatsos, I. 2005


distribution can be approximated by a polynomial of third degree, the value of N, can be

determined by:

(5.36)

where (TA and (TB are the stresses found by the uni-axial strain gages mounted as shown in

(Fig. 5.32). If a polynomial of fifth degree is required to approximate the total stress

distribution, then:

(5.37)

where point C, D and E are as shown in (Fig. 5.32). A similar procedure can be followed for

a beam subjected to bending load for beams with variable thickness cross-sections subjected

to axial loads, or for beams with constant cross-sections subjected to shear loads.

Such a study would provide a means of comparison of the available theoretical approaches,

but also the effect of temperature in the latest shipbuilding materials, as such type of

analysis has never been carried out in detail and no reference for modem high tensile steels

is available in the published literature that was investigated. Such study would form an

excellent PhD study focusing more on experimental investigation and the development of

techniques for accurately measuring thermal stresses and their effects on marine structures.

5.13.3 Methods of Alleviating Temperature effects on Ships

Since it is impossible to avoid many of the temperature effects discussed in previous

chapters of this thesis, thought must be given to avoiding serious failure of the structure due

to this cause. Possible methods which can be used and are suggested by the author include:

1. Greater use of insulating materials

2. The elimination of temperature stresses in regions of high stress due to loading or

wave effects

3. The use of material having a lower coefficient of expansion

Moatsos, I. 2005


4. The avoidance of unfavourable painting schemes

5. The use of sprays to maintain even temperature

Let us consider each one of these at a time.

Insulating MaterialsMuch research is at present being applied to the production of materials having good

insulation properties at low cost and it is possible that this may offer a solution to some of

the temperature problems arising from the carriage of hot liquids in ordinary ships as well as

in those vessels designed for extremes of temperature. Corlett (196) and Abrahamsen (1960)

in the 1960s discussed the properties of some of the materials available at the time from a

thermal effect and thermal stresses point of view and the application of such materials to

marine structures. The majority of these apply to all ships where insulation is used to restrict

thermal effects. The most important is the possibility of failure of the insulation (and of the

container) where the surrounding structure must be expected to withstand the full

temperature gradient. Various measures to provide secondary "defences" against this

occurrence have been suggested for liquefied gas carriers but only experience will show if

they are adequate. In normal vessels the steel must be of a quality able to withstand such an

accident or crack arresters inserted which will limit the spread of failure. Great care must be

experienced in the design stage to avoid the possibility of "bridge connections" between the

body at extreme temperature and the hull. There are indications that the positions where

piping and ventilating trunking penetrate decks, etc are often trouble spots in refrigerated

ships due to inadequate precautions. No attempt appears to have been made to insulate "hot

oil" carriers. In bitumen carriers a layer of solid bitumen rapidly forms on the inside of the

tanks and provides the insulating layer which may account for the small amount of trouble

which has been experienced in these ships where one might expect very high stresses. With

improved insulating materials, it is possible that similar protection may be possible in

tankers.

Elimination a/Temperature Stresses due to Loading and Wave Loading

Heating oil fuel tanks has often led to structural damage. Possible methods for reducing

thermal stress levels include insulation and the use of corrugated bulkheads to allow

expansion effects to be take up more easily. When the tank is bounded by the side shell on

one or more sides, notch tough steel should be used in those positions when tensile stresses

Moatsos, I. 2005


will occur on the tank boundaries. This is already common practice in tankers where notch

tough steel is required at the connections of bulkheads and centre girders to the shell. When

the tanks to be heated are towards the ends of the ship, the dangers of fracture are reduced

and no special precautions are required unless exceptionally high temperatures are used.

Materials with Lower Coefficients of Thermal Expansion

Although steels with much lower coefficients of expansion than mild steel are available,

their cost is so high that this could not seem an economic method of overcoming the

problem in the immediate future. Aluminium and its alloys is considerably worse than steel

in this respect.

Painting SchemesThe importance of paint colour in heat absorption and temperature stressing appears not to

be widely accepted amongst ship owners and the publication of data for a wide range of

paints would be useful to designers.

Use of SpraysBefore loading liquefied gas into tanks it is common practice with some operators to cool

the tank by fine sprays of the liquefied material in order to avoid conditions of thermal

shock. The same principle might be used to cool heated plating and to prevent excessive

thermal stresses in the deck and side above the waterline.

Moatsos, I.2005



Abrahamsen, E. 1960, "Special Ships for the Transport of Liquefied Gas from theClassification Viewpoint", European Shipbuilding, Vol. 9.

Benham, P.P., Hoyle, R., Editors, 1964, Thermal Stress, Sir Isaac Pitman & Sons Ltd.,London United Kingdom.

Bennet, W. 1929, "Great Lakes Bulk Freighters", Transactions of the Society of NavalArchitects and Marine Engineers (SNAME), Vol. 37, pp 12-23.

Corlett E.C.B, Lethard, J.F. 1960, "Methane Transportation by Sea", Transactions of theRoyal Institute of Naval Architects (RINA), Vol. 102, London, UK, pp 471-484.

Corlett, E.C.B. 1950, "Thermal Expansion Effects in Composite Ships", Transactions ofthe Institute of Naval Architects (RINA), London, UK Vol. 92, pp 376-398.

Du, Z.G. 1991, "Calculation Method and Comparative Evaluation of the Thermal Stressin Longitudinal Hull Structural Components", Shipbuilding of China, April, 1991.

Evans, J.H. (Ed), 1975, Ship Structural Design Concepts, Cornell Maritime Press.

Fair Isle Weather Station Web-Site, [Online, Internet], Available:

http://www.zetnet.co.uk/sigs/weather/, Accessed June 6th 2005.

Gatewood, RE. 1957, Thermal Stresses-With Applications to Airplanes, Missiles,Turbines and Nuclear Reactors, McGraw-Hill Book Co., New York, USA.

Gatewood, RE. 1960, Thermal Stresses, McGraw Hill Publications.

Goodier, J.N. 1937, "Thermal Stress", ASME Journal of Applied Mechanics, Vol. 4, No.1, March.

Goodier, J.N. 1957, "Thermal Stress and Deformation" ASME Journal of AppliedMechanics, Vol. 24, No.3, September.

Hechtman, R.A. 1956, "Thermal Stresses in Ships", Ship Structure Committee ReportSerial No. SSC-95, National Academy of Sciences-National Research Council, WashingtonDC, USA.

Heder, M., Josefson, B.L., Ulfvarson, A. 1991, "Thermal Deformations and Stresses inan OBO Vessel Carrying a Heated Cargo", Marine Structures, Vol. 4, 1991.

Hoyt, S.L. 1952, Metal Data, Reinhold Publishing Corporation, New York, USA.

Hughes, O.F. 1983, Ship Structural Design, A Rationally-Based, Computer Aided,Optimization Approach, New York, John Wiley & Sons.

Hurst, O. 1943, "Deflections of Girders and ship Structures: A Note on TemperatureEffects", Transactions of the Institution of Naval Architects (RINA), Vol. 85, pp.74-82.

IMarEST Technical Affairs Committee 2004, "Metocean features in the North Sea", TheJournal of Offshore Technology, Vol. 12, No.2, March/April.

Jasper N.H. 1956, "Temperature-Induced Stresses in Beams and Ships", ASNE Journal,USA, Vol. 68, pp 485-497.

Kaplan, P., Benatar, M., Bentson, J., Achtarides, T.A. 1984, "Analysis and Assessmentof Major Uncertainties Associated with Ship Hull Ultimate Failure" Report No. SSC-322,Ship Structure Committee, Washington DC, USA.

Moatsos, I. 2005

http://www.zetnet.co.uk/sigs/weather/,


Kaya, C.F., Gates, R. G. 1958, "Temperature Distribution in Fins and Other Projections,Including those of Other Building Structures, by Several Procedures", ASME Transactions,Vol. 80.

Levy, S., 1958, "Determination of Loads in the Presence of Thermal Stresses", Journalof Aeronautical Sciences, October.

Lewis, E.V., Zubaly, R.B., Hoffman, D., Maclean, W.M., Van Hoof, R. 1973, "LoadCriteria for Ship Structural Design", Ship Structure Committee Report Serial No. SSC-240,US Coast Guard, Washington DC, USA.

Lewis, E.V., Editor, 1988, Principles of Naval Architecture, Volume 1, Stability andStrength, The Society of Naval Architects and Marine Engineers (SNAME), USA.

Maulbetsch, J.L. 1935, "Thermal Stress in Plates", ASME Journal of Applied Mechanics,Vol. 2, No.4, December.

McAdams, W.H. 1960, Heat Transmission (Third Edition). McGraw Hill BookCompany.

Meikle, G., Binning, M.S. 1961, "The Effect of Heating Steels to Moderately ElevatedTemperatures", RAE Technical Note METI99.

Meriam J.L., Lyman, P.T., Steidel, R.F., Brown, G.W., 1958, "Thermal Stresses in S.S.Boulder Victory", Journal of Ship Research, Vol. 2, No.2.

Miller, N.S. 1961, "Temperature Stresses in Ships", Proceedings of the I" InternationalShip Structures Congress, Glasgow, Scotland, UK, pp 7-12.

Mounce, W.S., Crossett, J.W., Armstrong, T.N. 1959, "Steels for the Containment ofLiquefied Gas Cargoes", Transactions of the Society of Naval Architects and MarineEngineers (SNAME), Vol. 67, pp 423-446.

Ossowski, W. 1960, "Investigation of Thermal Stresses in a Tanker due to Hot CargoOil", BSRA Report No. 333.

Shi, W.B., Thompson, P.A., Le Hire, J.-C. 1996, "Thermal Stress and Hull StressMonitoring", Transactions of the Society of Naval Architects and Marine Engineers(SNAME), Vol. 104, pp 61-79.

Taggart, R. Editor, 1980, Ship Design and Construction, The Society of Naval Architectsand Marine Engineers (SNAME), USA.

Timoshenko, S. 1934, Theory of Elasticity, New York, McGraw-Hill Book Company.

Vasta, J. 1958, "Lessons Learned from Full Scale Structural Tests", Transactions of theSociety of Naval Architects and Marine Engineers (SNAME), Vol. 66, pp 165-243.

Vilner, A.C. 1986, "Development of Ship Strength Formulations", Proceedings of theInternational Conference on Advances in Marine Structures, Elsevier, London, UK, pp 152-173.

Vouthounis, P.A, 1993, Technical Mechanics-Strength of Materials, (In Greek), Athens,Greece.

Moatsos.L 2005


> -10'?

CROSS SrCT.O"1--TI.AT FRAME 58

-.O~

- I -

"I

+1000

_TEMPERATUAE DISTRIBUTION THERMAL STRESSON CROSS SECTION-PSI

Figure 5.1 Computed Thermal Stress in Shell & Deck Plating of T2 Tanker for different drafts withLBHD at 0°, (Hechtman, 1956).

$V" .aT "

CIIOSS SECTIONAT 'IIAM£ :18-'0'/

--10 ,

-1000

~TE"'PERATURE DISTRI8UTlON THERMAL STRESSON CROSS SECTION -PSI

Figure 5.2 Computed Thermal Stress in Shell & Deck Plating of T2 Tanker for different drafts withLBHD at 10°, (Hechtman, 1956).

1...1000

Moatsos, l. 2005


~"

PORT-720~ ___ ._

~.-.- ..

f: 0>.....,.,+ 0,

IIII

-1540 I -IOFV I

• I-. I1

'-..... Ir I.(II~j i\

s,I

l I~470: - . -~,- - -- - _,

-100

-170

TEMPERATURE fUSE a COMPRESSIVE

STRESS PLOTTED OUTWARDS

TEMPERATURE -- --- - ---- - - -- ---

STRESS

Figure 5.3 Computed Thermal Stresses in T2 Tanker with sun at Port Side, (Hechtman, 1956).

SOOB 1i:c:"" ":c:'"CE+§A &I::s::i .::1: N... a:- ...a:-

... --.+ ,t;t, .., ".. e

t, .. :t

C,

" a:~

:s ~ ...a: , ",;~,

u --- Deck Temp, B .."" I \~ao

§ .~ I ,(00--- STaD Temp, A .... , \,---Port. Temp, C

1-00 ,

1~I ,/\-.

0 I , \ "\

a, , '

0 I , \ \... I / ' 1.. I \ \.. • , ,.. u I,... c: / \

.: I , I,

III j.,.-,! I , \to I... II

I.. -0 ;'1 r'\, •

u .... , ,\... a:~ \ I F>; I ,..

00 1'1 I , \•-a to c I ~ / \ I,, \WI • ::I I \... ~a: I / \ "• "

,II

l I / \ • .. \:0: "I, -, I _--- ,..100 "

,•... J ' "'."",,.----~ / /'--

I ' ,0 /',' _,.- ---- -.."-__ _ L-.........,.---·

- _______ -::---.- .,..-.1- ...._---_#'.,

120

110 ;::t-Ilk::I

100 .....toE..(00

O~ ~ ~ ~ ~ ~ _.~

0000 0400 0800 1200 1600Time of D&y. (P. D. T.)

lOOO 2400

Figure 5.4 Temperatures and Radiation Control Plot, (Hechtman, 1956).

Moatsos, I. 2005


&a40000·CZ)..o~NO f 0r-: .- r - -.

t--l!~r~t

I 6' ITranmm ~ 11'---~+l -'/ Transverse

Test se~ction fl T• .) _j'~===! f Te.t Sectron

.. ------- ----o----1!~ r L~_-. I. ~- . .. lO:..----O----!.---'O---

For~ Ll~['lJ~Port !Starboard -i~·I"~-=6=':+=6=.~+-·t--~6~'---+·;~6:--'~F~ard

Starboard Side ShelllDngitudinal Section

II .,Q,I,;- --,,•~•,I

~•- --,_~

I•~,

I .,'

Port Side ShellLongitudinal Section

:~ ~//o--o---o-.- -,'O40 I

lOt ii' ii' t+--+_·-"_·_·'" 0 0 °r...._+-·- ..-·-·t~p -, ,- +9la. I I " \ I I la.o ~ • " \ .. I 0..0 6! " \ lc~ ~

• I ~ r: Itt 1 -; I I •~ • : ~ l+f'1 · " ..L+ I I v6.. j t. .J

T ~.t ~.2...._+ )$:: --0-- T Hull Plate Tem.perature .,

~...J31L-~i_~. kL.._L~:::iOF j=C)

Starboard

Test IIIDate: Aug. 9. 1957Time; 1335 PDTSky: Clear

Ship's heading: 326 deg trueSun'S azimuth: 186 degSun's altitude: 66 deg

Figure 5.5 Temperature Changes on Transverse and Longitudinal Test Section (Corlet, 1950).

Moatsos, I. 2005


r--sYM ABT er..

I ". I-- -10 Fi ~ /

I.~

•

I O·F~•

II

I ",--t ""IF'"

I (:,

•• ;n-../

Figure 5.6 Temperature Change in Transverse Section for 10°F Difference between Air & WaterTemperature (Hechtman, 1956).

6

-u... 14......"..::s.. ,,... ,.r- Red"Q, rE" rHtoo

"uIt... 10..::JII)

Time

Figure 5.7 Effect of Colour upon Temperature of Horizontal Surfaces Subjected to Insolation.(Hechtman, 1956).

Moatsos, I. 2005


o 10 ZO'C o S lOFT

DI"[lSIOJ$ COUITIONS

l.~ •• .- HI naU." 61.15nOt'nM ('TO u,.,.u otu) 3".75 nlrn SlC"tO~ ""10SM.n

CL... oliOT II1( MGOIf

WATtII Tlf'lpt"".,.1 66.0aFAA.'UT S.U£ TUlrtUTUII( 12.50FEII•• ~M lULl Sij)l HH"UUIUI( 84.S0fWftIH ItJ'-. UII U"pl,ufultt 16.00f

TemperaturefOT Plate ABC

/z..-rrTT1'1':'-""""r-rr"T""~~1 TZ

r--_~T

Figure 5.8 Temperature Gradient resulting from Difference in Colour Surface (Meriam et aI., 1958).

----x

Ternpe::rature

Figure 5.9 Schematic Diagram of three-dimensional Temperature Variation in Structural Corner

Moatsos, L 2005


Figure 5.10 Elementary Thermal Stress Material Definitions

IY"I ~

1 ~- --II

Tx = Tv:: Constant at any planeparallel to XZ plane

__ x

T z = T Y '" Constant at any pla.neparallel to XZ plane

Figure 5.11 Temperature Gradients in Beam with Rectangular Cross Section

Moatsos, I. 2005


y

Jill'"Bow

Figure 5.12 Idealized girder of Uniform Cross Section throughout its Length with Connections betweenthe Sides of the Box assumed Hinged

+y

--lD-Solution not

appncablehere

-z '-.x aas

Figure 5.13 Non Applicability of Thermal Stress Distribution Theoretical Solution Near the Ends ofBeam

Moatsos, I. 2005


1930 PliCompression

----- Temperotu .. ChonQe, de9 F

1,100 deQF.I Ref_ T....perotu ... • - . 40 deQ tllrouQflout Ship

__ --Stnts .~ (HIIIIPlatinQ)

r-~~0~i1

/

@"f 6710 PII \r: Tension ~ ---__'@

NflUlrol

Z

Aais ® '\ ",(comPuted) ,

3710psiCompression

• Tilt S,ctlon ~ ... t of t"rtil (,a - 1.314 )( lOa in4, lid I.,. - 2.706)( 10' in4

30,tDraft

1---- LonQitudlnot Bulkheads -----I

The SICUOIIAre, Of Stael A -.3393 in2

Figure 5.14 Assumed Symmetrical Temperature Distribution, (Jasper, 1956).

'/_____ Stress ClIonoe (HIIII Plo1ino)

~4000 PSi-+j -\_Iii ,...---

----- Temperolure Chono., deo F

,.100 deo F ., Reference Temperoture40 deo throuGhout Ship

5450 psiCompreSSion

3450 psi ITension I

I~--+J

////

Oil Level Inside Tank$(Some os WL Level)

y

I\ @l_,,,~ I\.,---------+®,\'\\\c--'\\\

5710 psiTension

30 ftDraft@

Lon(jitlldinol Bulkheads

2130 psiC_ion

The Sedion Yo ... nt of Inertia' o. - 1.314 )( 10' in4, and' "1- 2. 706)( 10' in4

The Section Arel of Steei A - 3393 ift2 Location of N. Axis 20' - 8.2"above B.L.

Figure 5.15 Assumed Asymmetrical Temperature Distributions, , (Jasper, 1956).

Moatsos, I. 2005


"0.1 'IoJM §oo€U.iA'*"'_' •• ~HC:'I"_

."."'.0 ,... ~u.~.... 'lMI~ .. l ~U'.l ..

!hip',i.udiJl,l )U"'.IN<*~ ..'.w ....u.: UftdclS~.' •• ldmd.t! 20 4q

Figure 5.16 Temperatures and corresponding thermal stresses on transverse and longitudinal testsections (Meriam et al., 1958).

Figure 5.17 Temperatures and corresponding thermal stresses on transverse and longitudinal testsections, Meriam et at. (1958).

Moatsos, I. 2005


...' e

.nree2. Stornoway3. Lerwick4. Fire Ness5. Bridllngton6. Sandett:le LV Auto7. Oreenwtch LV Auto8. Jerseyt. Channel LV Auto10. Scilly Auto11. Valentia12. Ronaldsway13. Malin Head

0_

Figure 5.18 Fair Isle Weather Station Location

Average Change In Temperature 78-98

12.0~1~1 Jw.".,

~?r10.0 "'" ~ ~ ~

~-I ¥.1. '\~

eT

8.0 I_;. ...,..

Degrees (oC) 6.0 VI

.L4.0 VI

J..20VI r-r-e-

l h..:&0.0 J..oJ..:..!

JAN FEB C,"" """MAR APR

~

MAY JUN JUL AUGMonth SEP OCT

ID A",rage 78.981

Figure 5.19 Monthly Average Diurnal Change in T (Fair Isle) 1978-1998.

Moatsos, 1. 2005


Air Temperature Fair Isle 1989

DegreesrC)

18.0

16.0

14.0

12.0

DECMonth

!C AWrag& 89 • Air Higwst Max. 0 Air Lowest Min.]

Figure 5.20 Monthly High, Low and Average Air Temperature (Fair Isle) 1989.

Cloud Cover Fair Isle during years of Extreme Temperature changes

1",989.,978 []1998 o 19921

Figure 5.21 Monthly Average Cloud Cover (Fair Isle) for Years of Average Extreme T Changes.

Moatsos, 1. 2005


Therrral Stresses TAlON FPSO(11.7"C Average Seasonal Durnal Terrp. OlangeScenario)

100 1 0

Figure 5.22 Average Seasonal Diurnal Thermal Stresses on Triton FPSO Structural Elements.

~zgQ)o

~is -2

-150

1 0

Figure 5.23 Extreme Summer Diurnal Thermal Stresses on Triton FPSO Structural Elements.

Therrral Stress.(l\VrTTlf)

Centerline

Moatsos, I. 2005

_ Qrtter Shell --Inner Shell _ rwvr Girders - Stringers

Therrml Stresses TATQ\J FPSO(16.01°C Extrerre SUmrer Durnal Terrp. O1angeScen r."

-150

lherrral Stress (I\VrTTlf)

_ Qrtter Shell --Inner Shell _ rwvr Girtders - Stringers Centerline


Therrral Stresses lATON FPSO(16.26 QC8<trerre Winter Durnal Terrp. OlangeScenario)

-150

Thermal Stress (NI ..... ·)

_ Outter Shell -Inner Shell _ twT Girders - Stringers Centerline

1 0

Figure 5.24 Extreme Winter Diurnal Thermal Stresses on Triton FPSO Structural Elements.

Therrral Stresses TRITONFPSO(17.21QC8<trerre Fall Durnal Terrp. OlangeScenario)

1 0

Figure 5.25 Extreme Fall Diurnal Thermal Stresses on Triton FPSO Structural Elements.

Therrml Stress (N'rTl'li)

_ QJter Shell -Inner Shell ~ NNf Girders _._ Stringers Centerline

Moatsos, I. 2005


lherrral Stresses TRITONFPSO(18.37"C Extrerre Spring Durnal Terrp. O1angeScenario)

150

lherrral Stress (N'rTfri?)

_ CAJterShell - Tank Top _.... NVVTGirders .....,_ Stringers Centerline

Figure 5.26 Extreme Spring Diurnal Thermal Stresses on Triton FPSO Structural Elements.

Utirrate Strength Variation due to lherrral Stress (Oetter Shell)TRITONFPSO24roOT-------~--------------------------------------------------,

19roo

E§.a:i 14roOQ)

£E0~Q)o 9roOc::

*i54roO

sU AJst 16.01

Figure 5.27 US Variation on the Outer Shell of the structure resulting from Diurnal Thermal Stressesfor all scenarios (TRITON FPSO).

_sUA'elherrral-sUAJst 11.7

_sUAJst 16.26 _sUAJst 17.21 --sUAJst 18.37

Moatsos, I. 2005


Utirmte Strength Variation due to 1herrml Stress (Inner Shell)'l"RTONFFSO

20000

'f~criQ) 15000

£EgQ) 100000c:(Ij

Uil5

5000

o so 100 1SO 200 2SO 300 350

Utirmte Strength (r-Yrrrrf)

_sU Pre Therrml--sU Fbst 11.7 sU Fbst 16.01

_ su Fbst 16.26 _ sU Fbst 17.21 -- sU Fbst 18.37

Figure 5.28 US Variation on the Inner Shell of the structure resulting from Diurnal Thermal Stressesfor all scenarios (TRITON FPSO).

Utirmte Strength Variation due to Therrml Stress (Centerline)'l"RTON FPSO

~z£gQ)oc:sCIlis

o so t:lO-soTherrml Stress (r-Yrrrrf)

-sU PreTherrml--sU FOst 11.7 sU Fbst 16.01

-sU Fbst 16.26 _sU Fbst 17.21 -sU Fbst 18.37

Figure 5.29 US Variation on the Centerline of the structure resulting from Diurnal Thermal Stresses forall scenarios (TRITON FPSO).

Moatsos, I. 2005


Nx

-H-'-tFigure 5.30 Strain Gauge beam definition.

h

LStress Dueto ExternalLoad

Self-Equilibrating T~tal StressThermalStreu

Figure 5.31 Combined Stress Distribution on Beam as a result of Axial Force.

Tt _j__ $-rIA-

o. ~l1h c--f h/l

!D-

1B--_j_

E_ _LO.211h 1 o. ll3hT T

Figure 5.32 Strain Gauge Location According to Polynomial Distribution.

Moatsos, I. 2005


Appendix 5, Tables

LOCATION AIR TEMPERATURE °C

PROBABLE MAX PROBABLE MIN

NNS 22° _5°

CNS 23° _6°

SNS 240 _7°

Table 5.1 Probable Maximum and Minimum Air Temperatures in the North Sea

LOCATION TYPICAL SEA TEMPERATURE °C

SUMMER WINTER

NNS 14.0° 7.0°

CNS 14.5° 6.0°

SNS 16.0° 5.0°

Table 5.2 Variations in Sea Surface Temperature

Temperature difference °cDeck

Colour

Black 10.00

Red 4.44

Aluminium -12.22

White -12.22

Table 5.3 Deck Colour Temperature Differences

Moatsos, I. 2005


Ultimate Strength Calculation - No Thermal Effects

Total Areas Oy Ou

m2 Nlmm2 Nlmm2

Outer Bottom 0.62586 311.56 235.01Inner Bottom 0.41549 315.00 220.23

Side 1.11719 289.00 197.73Deck 0.47935 347.93 199.12

DepthDB Height

21.200 m

2.200 m1437.5153742179.6260781197.099671-303.5111959

505.229682

0.40858

Depth of collapsed sides under compression10.860 m

the location of the N.A. above the B.L.

HoggingH

Depth of collapsed sides under compression1.176 m

the location of the N.A. above the B.L. 3352.39636650.6246588213.8181182

1894.8603

Table 5.4 US Calculation Sagging & Hogging, No Thermal Effects.

Ultimate Strength Calculation -11.7 -c Senario (Average Seasonal Diurnal Change In Temperature)

Total Areas ay au18.37m2 Nlmm2 Nlmm2 Depth 21.200 m

Outer Bottom 6.2586E-01 311.56 230.02 DB Height 2.200 m

Inner Bottom 4.1549E-01 315.00 205.22 863.47528

Side 1.1172E+00 289.00 151.83 2339.5534

Deck 4.7935E-01 347.93 104.56 7.7470E+02-95.009587183.503766

SaggingC1 0.15084913

Depth of collapsed sides under compression

15.140 m

the location of the N.A. above the S.L.

HoggingH


3.909 m

3310.65053653.495547494.7790221493.83064

the location of the N.A. above the S.L.

Table 5.5 US Calculation Sagging & Hogging, Average Seasonal Scenario.

Moatsos, I. 2005


Ultimate Strength Calculation -16.01 QCSenario (Extreme Spring Diurnal Change In Temperature)

Total Areas aym2 Nlmm2

Outer Bottom 6.2586E-01 311.56Inner Bottom 4.1549E-01 315.00

Side 1.1172E+00 289.00Deck 4.7935E-01 347.93

SaggingC1 0.045970732

au18.37Nlmm2

227.97199.41135.6470.52

DepthDB Height

21.200 m2.200 m

608.9605552303.707916.2113E+02-36.606511113.676863


16.519 m


Reduction

HoggingH


5.031 m

~.1%

3290.0483662.479926552.3920241356.59266


Table 5.6 US Calculation Sagging & Hogging, Extreme Summer Scenario.

Ultimate Strength Calculation -16.26 QCSenario (Extreme Spring Diurnal Change In Temperature)

Total Areas ay au16.26m' Nlmm' Nlmm2 Depth 21.200 m


Inner Bottom 4.1549E-01 315.00 198.95 598.565119

Side 1.1172E+00 289.00 134.76 2298.80086

Deck 4.7935E-01 347.93 69.17 6.1397E+02-34.323826110.869522

SaggingC1 0.040568965C2 8.1819E-01H 4.616978225


16.583 m

the location of the N.A. above the B.l.

HoggingH


5.100 m

the location of the NA above the B.L. 3.2881E+03662.931561555.5688481348.22982

Table 5.7 US Calculation Sagging & Hogging, Extreme Winter Scenario.

Moatsos, I. 2005


Ultimate Strength Calculation -17.21 DCSenario (Extreme Spring Diurnal Change In Temperature)

Total Areas ay au17.21m2 Nlmm2 Nlmm2 Depth 21.200 m


Inner Bottom 4.1549E-01 315.00 197.71 537.744642

Side 1.1172E+00 289.00 131.17 2280.98453

Deck 4.7935E-01 347.93 61.58 5.8187E+02-24.73924498.8659641

SaggingC1 0.01605766

C2 8.1819E-01H 4.338492852

2.984


16.862 m


37.3 '"

HoggingH


5.360 m

the location of the N.A. above the B.l. 3.2834E+03665.778646565.01099

1317.89736

Table 5.8 US Calculation Sagging & Hogging, Extreme Fall Scenario.

Ultimate Strength Calculation -18.37 DCSenario (Extreme Spring Diurnal Change In Temperature)

Total Areas ay au18.37m' Nlmm' Nlmm2 Depth 21.200 m

Outer Bottom 6.2S86E-01 311.56 227.17 DB Height 2.200 m

Inner Bottom 4.1549E-01 315.00 196.66 447.829988

Side 1.1172E+00 289.00 125.97 2248.71043

Deck 4.7935E-01 347.93 50.65 5.3738E+02-13.46614483.501999

SaggingC1 -0.02009836

C2 8.1819E-01H 3.957207663


17.243 m


40.8%

HoggingH


5.718 m

the location of the N.A. above the B.l. 3279.46075671.45225

573.7894021278.20227

Table 5.9 US Calculation Sagging & Hogging, Extreme Spring Scenario.

Moatsos, 1. 2005


Appendix 5, Additional Theory

Thermal Strains and Stresses in an unstressed bar.

For an unstressed bar fitted between two rigid supports, as the temperature of the bar

increases, no longitudinal strain occurs because the bar is restrained. The thermal stress

developed corresponds to the strain which would have taken place if the bar had been free to

expand.

Assuming that the same bar for the given temperature rise would elongate an amount .1 if

free to expand and that the distance between the rigid supports is longer than the bar by the

amount 0.4.1. As the bar expanded under increasing temperature to close this gap, a thermal

elongation of 0.4.1 would be observed; but no thermal stress would be developed on the bar.

However, as the bar continued to expand beyond this point to its final temperature, no

additional thermal strain would be observed; but a thermal stress proportional to the

elongation, (.1-0.4.<:1)or 0.6.1, which the bar was restrained from developing, would occur. A

somewhat similar situation would exist if instead of a gap the bar was attached to adjacent

deformable members. The thermal stress in the bar would be proportional to the portion of

the free temperature expansion which was prevented by the attached members from

occurring.

A distinction should be made between the strains arising from a change in temperature and

the strains resulting from external loads. In the latter case, the stresses are proportional to

the strains. By contrast, thermal stresses arise when the thermal strains are inhibited. It is

important to recognize that the thermal strains observed in ships represent the free

expansion part of this process and cause no stress but rather are manifested in elongation

and bending of the hull. When considered together with the temperature distribution, the

measured thermal strains can be used to determine the amount of thermal strain which has

been prevented from occurring by the rigidity of the surrounding structure. This amount

determines the actual thermal stress.

Now suppose that the bar was a flat rectangular plate restrained on all four edges by rigid

supports so that the expansion in its plane would be impossible. A uniform temperature rise

would tend to cause expansion in the longitudinal and transverse directions and therefore

Moatsos, I. 2005


biaxial compressive thermal stress. Moreover, because of Poisson effect, each longitudinalI

component of stress would produce an additional compressive stress in the transverse

direction and vice versa. Thus, either of the components of biaxial stress in this last case

would be greater than the longitudinal stress developed by the same temperature increase in

the original bar. Since the panel of plating in a ship ordinarily has restraints on all four

edges, a condition approaching the one just described occurs. For complete restraint in the

axial direction only, the thermal stress a for uniform temperature change T in a bar where

no bending occur is:

a=-EaT (A.5.1)

where a is the coefficient of thermal expansion. For partial restraint in the axial direction Eq

(A.S.!) becomes:

a =Ee-EaT (A.S.2)

Where e is the observed thermal strain.

For a rectangular flat plate partially restrained on the four edges and subjected to uniform

temperature changes, the biaxial thermal stresses are:

E ( ) EaT(j =-- e +ve ---

x l-v2 x Y I-v

E ( ) EaT(j =-- e +Ve ---

Y l-v2 Y x I-v

(A.S.3)

Moatsos, I. 2005

CHAPTER6

ULTIMATE STRENGTH OF SHIP STRUCTURES

6. 1 Introduction

Recent years have seen the growth of interest in the ultimate strength of ships' hulls and in

related problems of nonlinear behaviour and Elasto-plastic collapse of ships' structural

elements. Research in this area has contributed to the development of limit state design

methods and quantitative reliability analysis which require explicit consideration of ultimate

limit state (collapse) conditions. Research into the mechanics of structural failure has been

stimulated since the early 1980s, according to Smith (1983), by the growth in power of

computers, which has allowed effective numerical treatment of previously intractable

nonlinear problems. Systematic numerical studies, based usually on finite element or similar

techniques and supported in some cases by experimental data, have led to a much improved

understanding of the collapse behaviour of stiffened and unstiffened plates and shells. The

importance of structural imperfections, including particularly initial deformations and

residual stresses caused by welding and cold forming, has become generally recognized, as

has the need for a statistical definition of such imperfections and their effect on strength. It

has also been recognized that the performance of a redundant structure such as a ship's hull

or an offshore platform may be generally affected by pre-collapse load carrying capacity of

structural components. Evidence of the importance of imperfections has led to investigation

of damage conditions, as may be caused in a ship by collisions, grounding, hydrodynamic

overload or weapon effects, and to recognition of a need for damage-tolerant structural

designs.

Previous studies on the development of a formulation for ultimate hull strength prediction

may be classified into three groups, as described in (Chapter 3) during the critical review of

this study:

1. The first is a linear approach where the behaviour of the hull up to failure of the

compression flange is assumed to be linear elastic, Le. ignoring buckling, and the

ultimate moment capacity of the hull is basically expressed as the ultimate strength

of the compression flange multiplied by the elastic section modulus, with a simple

Moatsos, I. 2005

Chapter 6. Ultimate Strength 200

correction for buckling and yielding, as it can be seen in (Valsgraard & Steen,

1991), (Vasta, 1958) and (Viner, 1986).

2. The second is an empirical approach, where an expression is derived on the basis of

experimental or numerical data from scaled or real hull model tests, as it can be

seen in (Faulkner & Sadden, 1979), (Frieze & Lin, 1991) and (Mansour et al.,

1995).

3. The third is an analytical approach, based on a presumed stress distribution over the

hull section (plane sections remain plane) from which the moment of resistance of

the hull is theoretically calculated, taking into account buckling in the compression

flange, as it can be seen in (Caldwell, 1965), (Paik & Mansour, 1995) and (Paik et

al. 2001).

The first approach is quite simple, but its accuracy is usually wanting as after buckling of

the compression flange, the behaviour of the hull is not longer linear, and the neutral axis

changes position. The second approach of empirical formulations may provide reasonable

results for conventional hulls, but one has to be careful when using such an approach for

new and general-type hulls, since they are usually derived on the basis of limited data, or for

a particular hull form. On the other hand the third approach of analytical formulations can

be applied to new or general hulls as they include section effects more precisely. The ship

hull ultimate strength formula is eventually expressed as a function of design parameters

related to geometric and material properties including plate thickness, yield strength and

Young's modulus. When time-variant structural degradation, as such as corrosion or

fatigue, is considered, the value of member thickness at any particular time is a function of

such damage. In probability-based design methods, all the design parameters are treated as

the random variables and the hull ultimate strength formula is normally different from that

fro sagging.

The strength of stiffened plating forming the shell and deck structure of a ship's hull

depends critically, particularly under compressive load, on the behaviour of individual

rectangular plate elements contained between stiffeners. Such plate elements are normally

bounded at their sides by closely spaced stringers aligned in the direction of the dominant

load and at their ends by relatively widely spaced transverse frames. The strength of a

stiffened shell is influenced not only by the collapse strength (maximum load carrying

Moatsos, I. 2005


capacity) of plate elements but also by the pre-collapse loss of stiffness resulting from

elastic buckling and/or yielding.

In the task that a ship structural designer faces when deciding what primary ship structural

characteristics are acceptable three important aspects need to be considered according to

Faulkner (1972):

i. Fracture: brittle, by fatigue or by low-energy propagation.

11. Ultimate load: the inability to carry further load in the cross section due to general

tensile or compression failure.

111. Excessive stiffness or limberness: vibration (comfort or equipment malfunction),

alignment, vibratory bending perhaps augmenting quasi-static ship bending, and

fatigue.

In this study emphasis is placed on the second point as in the case of failure, ship loss is a

possibility. Tensile yielding in metals can be easily evaluated and stated in statistical terms

but the role of compression and its importance in the cross-section elements produces two

major uncertainties:

a. The true compression strength of stiffened plates in the presence of lateral pressure

and some in-plane transverse compression and in-plane shear and bending is a

subject that is yet to be properly understood. Compression strength is subject to a

large amount of statistical variance and residual strength degradations.

b. The failure of compression elements to sustain a high enough portion of their

maximum load after this has been reached, so that elasto-plastic buckling actions

may be considered through entire cross sections, creates a number of difficulties

which arise from the observed rapid fall in load capacity beyond the collapse strain.

We consider the capacity of the structural member being reached moment as having been

reached when the first sizable and important element of the ship's cross section reaches its

maximum compression load. Hence n the design of the hull bottom, of a ship structure, and

of the strength deck, in particular, compression strength is the key parameter and inelastic

buckling considerations determine the behaviour. The fact that indications from calculations

Moatsos, I.2005


show that extreme loads sagging wave bending moments may be appreciably higher that

hogging ones places even more emphasis on the importance of compression.

Although research on stiffened plate behaviour started as back as the last century, a large

number of theoretical and numerical studies on both stiffened and unstiffened plate

behaviour have been carried out since 1970. As it can be seen in the Appendix (Fig. 6.1)

shows a typical stiffened plate consisting of plate and longitudinal stiffeners as well as

transverse stiffeners (girders). The failure modes of a stiffened plate are:

1. Plate Failure

2. Stiffener-Plate Column Failure which can be divided into two modes:

a. Plate Induced Failure

b. Stiffener Induced Failure

3. Torsional Failure of the Stiffener

4. Overall Grillage Buckling

Plate failure may occur before or after the failure of column-like failure, which affect the

stiffness and the effective width of the plating associated with the stiffener. Failure modes 3

and 4 should be avoided as they result in quick loss of strength in the post-buckling region.

For preventing Torsional buckling, the ratio of the web height to thickness is generally kept

to less than 10. Overall grillage buckling is usually avoided by provision of stiff transverse

frames and support from minor bulkheads and pillars.

6.2 Uncertainties in the calculation of US

Any methodology used for the determination of the US of either stiffened-un stiffened plates

or of the overall hull girder is subject to a number of uncertainties both with respect to

construction and to the analytical procedures used. Uncertainties associated with the

construction include variability of material properties, construction tolerances and the

effects of in-service damage. The effect on the results that these might have will be briefly

discussed in the next paragraphs and their effects are incorporated in the analysis performed

either through the formulations and approaches used or via the stochastic modelling of the

variables used in the limit state equation for reliability analysis.

Moatsos, I. 2005


Although all material properties will affect the yield strength of a hull is some way or

another, the influence of yield strength is probably the most significant. A study by

Wickham & Hart (1984) on the variability of this parameter indicates that the mean and

standard deviation found within batches vary between mills and are dependent on thickness.

In the latter case, the additional working of material required for the production of thinner

plating has been found to enhance the strength but at an expense of greater variability.

During the fabrication process, imperfections are induced in the structure in the form of

local distortions and residual stress. Both are functions of the welding process and have an

influence on local strength. High tensile stresses which develop in the vicinity of a weld due

to shrinkage are balanced, according to Rutherford & Caldwell (1990), by non-uniform

compressive stresses across the plate. These compressive stresses affect the yielding process

and hence reduce the pre-collapse stiffness of the structure. Depending on the slenderness of

the plate involved, the collapse strength may also be affected. The level of residual stress in

a new ship may well be modified in service by the loading and subsequent unloading which

occurs with bending of the hull. Under the application of a tensile stress, the edge zones

which are already at yield will strain at constant stress while the remainder of the plate

carries the entire applied load. When the plate is unloaded, a modified self-equilibrating

stress pattern will have formed where both the tensile and compressive residual stresses are

reduced. The influence of residual stresses during our analysis is assumed as described by

the theories and approaches described in the subsequent sections of this chapter and will be

described in details in each case for stiffened and unstiffened plates. In certain cases forms

part of the formulations or in the case of regression equations based on tests in somehow

assumed as "built-in" the coefficients that form the equations.

The one-sided welding process used in fabrication generally causes a dishing of plate panels

between longitudinals together with a bowing of the stiffened panels between frames. The

main effect of such distortions is to produce out-of-plane deflections from the onset of

loading which influence the stiffness of the structure and hence the collapse strength. The

prediction of imperfections is uncertain both with respect to magnitude and direction since

the final shape of the structure depends not only on the welding process but also on the

shape of individual components prior to welding. The initial bow of a stiffening member

will tend to force the plating to develop a similar bow which may oppose or add th the

imperfection caused by weld shrinkage.

Moatsos, I. 2005


6.3 Behaviour of Unstiffened plates

As part of a stiffened panel, plate elements are commonly used as structural components in

ships and marine structures. Since the global failure of a stiffened panel is usually avoided

by design, the inter-frame failures of the plate elements between stiffeners are the main

failure modes and hence the prediction of the plate strength is a prerequisite for assessing

the strength of a stiffened plate.

6.3.1 Parameters influencing strength

The most important parameters influencing the strength of unstiffened plates are:

• Plate slenderness as it results from the non-dimensional variable that results from the

Bryan expression for the critical buckling load (J'c of an infinitely long thin, elastic

plate with simply supported edges and which is the most important factor:

(6.1)

• Residual stresses that arise from the fact that plates are welded components of

structures

• Initial distortion which gives rise to a decrease in the rigidity and ultimate strength

of plates.

• The boundary conditions which are classified into two extreme conditions: simple

and clamped supports. For unloaded edges, the conditions are grouped into three

subgroups: constrained, restrained and unrestrained. In the first two cases the edges

are forced to remain straight, something that does not happen in the unrestrained

case. For restrained conditions no displacements are allowed in the transverse

direction, whereas they are allowed for the other two cases.

• The aspect ratio of the plate, the ratio of the plate length over the plate breadth.

• The combination of the loads imposed on the plate with the ones generally

considered being: longitudinal compression, transverse in-plane compression, shear,

bending moment and lateral loading. Although the effect of combined loading can

be reasonably predicted by numerical methods, these can be improved much further.

Moatsos, I.2005


6.4 Behaviour of stiffened plates

Due to the interaction of the different failure modes, the situation is rather complicated. As

already discussed in the introduction of this chapter, Failure modes 3 and 4 are excluded by

properly selecting the dimensions of the stiffened plates and the behaviour of the stiffened

plates can be represented by an assemblage of the stiffener and its associated plate with

effective width. The behaviour of the assemblage can be exactly (in a purely mathematical

sense) analysed by a numerical method, such as the finite difference or finite element

methods. It has been suggested by Smith et al. (1991) and Chalmers and Smith (1992) that

numerical methods could be directly used in design in such a way that the entire load

shortening curves generated and stored in a computer facilitate in the calculation of the

ultimate strength of a stiffened plate by interpolation of the stored data. Numerical methods

have also been used to establish safety margins equations is reliability analysis as

demonstrated by Bonello and Chryssanthopoulos (1993).

Although is likely that numerical analysis in the form of FE techniques could be directly

used in design in the near future, as a result of the reduction of. costs and increase of

processing power of modem computer systems, nevertheless relatively simple analytical

formulations are still the preferred design practice at the moment

6.4.1 Parameters influencing strength

The parameters might be classified as geometrical and imperfection parameters, according

to Das (2004). The main geometrical parameters which influence the strength are as

follows:

Geometrical Parameters

• Stiffener slenderness A

• Plate slenderness p• Ratio of stiffener to cross-sectional Area A/At

• Ratio of top flange to web area AIAw

• Cross-Sectional slenderness of the stiffener.

Moatsos, I. 2005


Uncertainty Parameters

• Initial stiffener deflection 4Js• Relative stiffener deflection 4Js/4Js2• Initial plate deflection 4J• Compressive plate welding stresses arp

• Axial welding stresses in the stiffener ars

• Yield stress ao

When formulating the ultimate strength of stiffened panels, two important issues involved in

the selection of different parameters in the design formula should be considered.

a) Determination a/the Effective Width/or the Stiffened Plate

Although there are some good formulae to determine the effective width in maximum

compression of the plate, there are few formulae to calculate the effective width when

the compression is below the maximum compression. Unfortunately, for plates with

moderate residual stress, the maximum strength a reached for in plane compression

when tiC{F 1.5-2.0, while, except for very stocky stiffeners, the stiffener itself will

collapse by compressive yielding in top of the stiffener before the plate has reached its

maximum load. Therefore from the theoretical point of view, the effective width should

be determined by iterative equilibrium analysis or incremental analysis.

b) The Interaction between Adjacent Stiffener Spans

The primary interaction effect between adjacent stiffener spans is due to the plate flange

buckling causing larger reduction in out-of plane stiffness for the stiffener element

deflections away from the plate flange than that for the adjacent elements deflecting in

the opposite direction. The former element will thereby cause deteriorating end

moments on the stiffener-induced elements and itself somewhat restrained by the end

moments

The increased out-of-plane deflection magnification due to plate buckling may be

considered as the result of:

i. Reduced effective Euler stress giving larger magnification factor

Moatsos, I. 2005


11. Eccentricity of end loads due to larger buckling induced shift of neutral axis at the

midspan rather than at the ends

lll. Restraining end moment due to smaller lateral deflection in the stiffener induced

span.

The eccentricity effect could be treated as a modified initial stiffener deflection.

6.S Ultimate Strength of Unstiffened and Stiffened Panels existing literature.

A number of methods have been proposed for the evaluation of the ultimate strength of

unstiffened and stiffened panels. For unstiffened panels a number of methods employing

empirical solutions have been available for a number of years. Work by ViInay (1981)

proposed a generalised effective width formula and Rhodes (1981) employed a simple

method to generate the load shortening curve of a plate loaded in compression showing

good agreement with results from numerical methods but not so good for imperfect plates

with large deflections. If we focus our attention to design oriented methods, most notable

work includes work by Faulkner (1975), Carlsen (1977), Bonello (1991) and Guedes Soares

(1988). In a comparison between the methods according to Das (2004), Guedes Soares

(1988) approach produces the best result when the methods were calibrated against existing

experimental and numerical data. For stiffened panels, most notable work includes formulae

proposed by Faulkner (1975), Carlsen(1980), Imperial College (1991) and Das and Pu

(1994). In a comparison between the methods according to Das (2004), as it can be seen in

the appendix (Table 6.1), Faulkner (1975) method produces the best result with the mean

value of 1.041 and coefficient of variation of 11.7 % when the methods were calibrated

against existing experimental and numerical data.

6.6 Ultimate Strength of Hull Girders existing literature.

Previous studies on the development of a formula for the ultimate strength can be classified

into three groups:

1. The Linear Approach: The behaviour of the hull up to collapse of the compression

flange is assumed to be linear elastic without buckling, and the ultimate moment

capacity of the hull is basically expressed as the ultimate strength of the compression

flange multiplied by the elastic section modulus with a simple correction for

Moatsos, I. 2005


buckling and yielding. Work using the particular approach has been published by

Vasta (1958), Mansour and Faulkner (1973), Viner (1986) and Valsgaard and Steen

(1991). The approach is quite simple but accuracy might not be good as a result of

the non linear behaviour of the hull and the change in position of the neutral axis

after buckling of the compression flange.

2. The Empirical Approach: An expression is derived on the basis of experimental and

numerical data from scaled hull models. Work using the particular approach has

been published by Faulkner and Sadden (1979), Frieze and Lin (1991) and Mansour

et al. (1995). Empirical formulations may provide reasonable solutions for

conventional hulls but one has to be careful in using empirical formulations for new

and general type hulls since usually they are derived on the basis of limited data.

3. The Analytical Approach: The approach is based on a presumed strain distribution

over the hull section (plane cross section remains plane), from which the moment of

resistance of the hull is theoretically calculated taking into account buckling in the

compression flange and yielding in the tension flange. Work using the particular

approach has been published by Caldwell (1965), Paik and Mansour (1995).

Analytical formulations can be applied to new or general hulls since they include

section effects more precisely

6.7 Modelling the Ultimate Strength of Hull Girders

Before the method proposed by the author is described, a comparative study of various

existing methods was performed to determine which of the most accurate methods can be

effectively combined to form the suggested procedure. The Faulkner (1975) stiffened panel

ultimate strength formulation and Guedes-Soares (1988) unstiffened plate formulation was

combined with Paik's(l997) work on Stiffened Plates and the Paik, Hughes and Mansour

(2001) closed form formulation for the determination of the ultimate strength of the entire

hull girder and compared with a modified Smith (1977) approach. Each approach will be

described in detail in the following sections.

6.7.1 Guedes Soares (1988) UnstifTened Panels Analytical Method

For the determination of the ultimate strength of a plate from the comparison of the existing

methodology, according to Das (2004b), the Guedes Soares (1988) approach was selected

Moatsos, I. 2005


as being the most accurate. As described in Guedes Soares (1988) the method presented has

two forms and accounts explicitly for p, 1], and &:

~ = (1.08~,(1.07 - 0.99 <l.:,11- (0.626 -0.12IP)~' 10.76 + 0.0111+ 0.24 ~' +O.lp) for P > 1.0

9= (1.08¢,{(1- 1~:~}1 +0.007817)II-(0.626-0.12IP)~' 10.665+0.00611+0.3<' +0.14P)(6.2), (6.3)

The terms in the first brackets predict the strength of perfect plates, the first and the second

predict the strength of plates with residual stress, the first and third indicate the strength of

plates with initial deflections and the four terms are used for plates that have both initial

deflections and residual stress. The terms ~. the strength of an unwelded plate and L1~, the

reduction of strength due to the weld induced residual stress, are calculated as follows:

(6.4)

where E is the Young's Modulus of Elasticity and p the plate slenderness ratio is calculated

from:

(6.5)

and the boundary condition constants ai, az are:

al = 2.0 and a2 = 1.0 For simple supports

al = 2.5 and a2 = 1.56 For clamped supports

(6.6a)

(6.6b)

The residual stress, O"r can be obtained from:

O"r 21]-=---=--

ay m-211 (6.7)

Moatsos, I. 2005

Chapter 60 Ultimate Strength 210

Where 1] is the yield tension block coefficient which varies for as built and after shakedown,

the progressive reduction is residual stresses arising from applied stresses in service:

405< 1] < 600 , for as built

300< 1] < 405 ,for after 'shakedown'

(608a)

(608b)

Also the Tangent Young' modulus Et is given from:

(609a)

(609b)

in which the proportional limit stress op:

ap -arP =r a

y

(6010)

According to Faulkner (1975), Pr is generally adopted as 0.5.

The boundary constants a3 and a4 are again for simply supported and clamped supported

plates:

a3 = 3.62 and a4 = 13.1 For simple supports

a3 = 6.31 and a4 = 39.8 For clamped supports

(6.lla)

(6.11 b)

As it can be seen from the theoretical description of the work in Guedes Soares (1988),

these equations should only be applicable to simply supported plates but whenever the

correct boundary conditions are used according to the particular coefficients in (Eq. 6.6), to

quantify l/Jb these can also be applied to clamped plates.

Moatsos, I. 2005


One can also not fail to notice that the most striking disadvantage of the method is the fact

that the maximum strength is estimated while ignoring the strain at which the maximum

values occur, which is very important for the case of sharp load shortening curves.

6.7.2 Faulkner (1975) Stiffened Panels Analytical Method

The Faulkner (1975) work is based on the Johnson-Ostenfeld formulae and the ultimate

strength of a stiffened panel is expressed as:

(6.12)

where:

O"e =1_'!_O"Y

=. 40"E

O"e 0"E-=-

0"E ~ 0.50" y(6.13)

In the aforementioned formulae we define O"u as the ultimate strength of the stiffened plate,

OJ the yield strength of the stiffened plate, As the area of the stiffener, t the thickness of the

plate and O"E the elastic strength of the stiffened plate. be is the effective breadth of the

stiffened panel, a definition of which is given in (Eq. 6.17) . O"E is defined as:

(6.14)

where a is the length of the plate and ree is the effective tangent radius of gyration defined

as:

(6.15)

Moatsos, I. 2005


and El,' is the buckling flexural rigidity of the stiffener. The tangest effective width of the

plate be' is given by:

b; =_1 Rb Pe r

b; =Rb r

(6.16)

where Pe is the effective plate slenderness ratio.

The effective width of the plate be is related to the plate slenderness ratio as follows:

(6.17)

Pe < 1

where:

(6.18)

R =1-[ 277 ]( p2 J~

r b _ 277 2P -1 Et

P ~ 1

R =1-[ 277 ]~r b E

--277t

(6.19)

P < 1

and:

Moatsos, I. 2005


Et ( 3.62p2 )2E= 13.1+0.25p4

Et =1E

(6.20)

P>2.7

6.7.3 Paik and Thayamballi (1997) Empirical Formulation

Paik and Thayamballi (1997) derived a simple empirical formulation based on test data by

Home et al. (1976) and (1977), Faulkner (1977), Niho (1978) and Yao (1980) and tests on

an additional series of 12 longitudinally stiffened plates with three different slenderness

value to improve an approach originaUy proposed by Lin (1985). The formulation suggested

by Lin (1985) is expressed in terms of the plate slenderness ration and the column (stiffener)

slenderness ratio and takes the following form:

(6.21)

where CrC5 are the test constants, p the slenderness ratio of plating between longitudinal

stiffeners given from (Eq. 6.5), 1 the column slenderness ratio of stiffener with full plating

given from:

(6.22)

in which a is the length of the longitudinal stiffener between transverse support frames and r

is the radius of gyration of one longitudinal stiffener including associated full plating given

from:

r=~ (6.23)

Moatsos, I.2005


in which I is the moment of inertia of one longitudinal stiffener including associated full

plating and A is the cross-sectional area of one longitudinal stiffener including associated

full plating. The moment of inertia I is given from:

(6.24)

in which Zo is the neutral axis height given from:

(6.25)

with b the stiffener spacing, tp the thickness of the plating, li; the height of the stiffener web,

bf the breadth of the stiffener flange, tf the thickness of the stiffener flange. The areas A and

Ast of the stiffener alone are calculated from:

A =btp +As,

As, = hwtw+bftf(6.26), (6.27)

With the analysis of the existing and new supplementary collapse test data, Paik &

Thayamballi (1997) determined the following improved set of constants by using the least

squares method:

Cl =0.995,c2 =0.936,c3 =0.176,c4 =0.188,c5 =-0.067 (6.28)

and substitution of (Eq. 6.28) into (Eq. 6.21) yields a new uni-axially stiffened plate

ultimate strength formula given by:

(Tu 1--=-r============================~O.995+0.936A? +O.170p2 +O.188A?P2 -0.067A_4

(6.29)

Moatsos, I. 2005


6.7.4 Hull Girder Ultimate Strength Models

Ship hull structures in the intact condition will sustain applied loads smaller than their

design loads, and in normal sea loading conditions .structural damages such as buckling and

collapse will not occur except for possible localized yielding according to Paik, Hughes and

Mansour (2001). Due to rough seas though or unusualloadinglunloading of cargo a certain

degree of uncertainty exists. Applied loads then could exceed design loads and the ship hull

structure could collapse globally. In addition to this, in the case of ships already in service

having suffered structural damage due to corrosion and fatigue the structural resistance may

have weakened as a result of such phenomena and the hull may collapse under applied loads

even smaller than the design loads. Most classification society criteria and procedure for

ship structural design are based on first yield of hull structures together with buckling

checks for structural components and not for the whole structure. This type of analysis has

proven to be effective for intact vessels in normal seas and loading conditions. Also ultimate

strength collapse could generally occur during storms where the difference in air and sea

temperatures is less than the one that occurs during sunny days and therefore showing that

the temperature effect is smaller. It is important to determine the true ultimate strength of a

ship hull girder if one is to obtain consistent measures of safety, which can form a fairer

basis for comparisons of vessels of different sizes and types. Ability to better assess the true

margin of safety should also lead to improvements in regulations and design requirements.

6.7.5 Paik and Mansour (2001) Analytical Approach

The approach is based on the analytical closed form expressions originally developed by

Caldwell (1965). The improvements lies in the fact that the original Caldwell formulation

assumes that the material of the entire ship hull in compression has reached its ultimate

buckling strength and full yielding occurs for the material in tension. The Paik and Mansour

(2001) approach has been derived based on the assumption that in the vicinity of the final

neutral axis the side shells will often remain in the elastic state until the overall collapse of

the hull girder takes place, while the flange and part of the side shell undergo compression

collapse and the other flange and part of the side shell yield.

Moatsos, I. 2005


To analytically describe the approach for hull girder bending design, it is of interest to

calculate linear first yield and full plastic bending moments of ship hulls under vertical

bending, which does not accommodate buckling collapse. An idealised hull section is

shown in (Fig. 6.2) with equivalent sectional areas at deck, outer bottom, inner bottom and

side shell. All longitudinal stiffeners are smeared into the related plating. Vertical or

horizontal sectional areas replace inclined member sections. All inner side plating and

longitudinal bulkheads are regarded as side. The section moduli of the equivalent hull can in

this case be given as follows:

Z - Zz Z _ ZzD - 'B-D-g g

(6.30), (6.31)

Where,

(6.32)

(6.33)

ZD and ZB, are section moduli at deck and outer bottom respectively. AD, AB and AB! are total

hull sectional area at deck, outer bottom and inner bottom respectively, while As is half of

the total hull sectional area for side shell including all longitudinal bulkheads. Until the

outermost fibre of the hull section in the ship depth direction yields, distribution of

longitudinal axial stresses in a hull section is linear elastic as shown in (Fig. 6.3). Linear

first yield moments (immediately after deck or outer bottom yields) can be calculated by:

(6.34), (6.35)

Where MyD and MyB are first yield hull girder moments at deck and outer bottom,

respectively, O"oD and o;JB are material stresses of deck and outer bottom respectively.

Moatsos, I.2005


After the equivalent hull section reaches the fully plastic state without buckling collapse as

shown in (Fig. 6.4), the full plastic bending moments (denoted by Mp) can approximately be

given by,

Where

(6.37)

a,.JB[, O"osu and (J'oSL are material yield stresses of inner bottom, upper side shell and lower

side shell, respectively.

The collapse of the compression flange governs the overall collapse of a ship hull under

vertical bending moment as shown by reassessment of actual failures according to Faulkner

et al.(1984) and according to numerical studies of full scale ships by Kutt et al. (1985),

Rutherford and Caldwell (1990), Valsgaard and Steen (1991) and Beghin et al. (1995)

amongst others, there is still some reserve strength beyond collapse of the compression

flange as a result of hull cross section neutral axis movement toward the tension flange,

after the collapse of the compression flange, and a further increase of the applied bending

moment is sustained until the tension flange yields. At later stages of the process, side shells

around the compression and the tension flanges will also fail. However in the immediate

vicinity of the final neutral axis, the side shells will often remain in the elastic state until the

overall collapse of the hull girder takes place. Depending on the geometric and material

properties of the hull section, these parts may also fail.

Paik and Mansour (1995) derived an analytical closed form expression for predicting the

ultimate vertical moment capacity of ships with general-type hull sections by using an

longitudinal stress distribution approach in the hull cross section at the moment of overall

collapse. In the compressed parts of the section, the hull girder flange and a part of the side

shell are at their ultimate compressive limit. In the flange parts of the section subjected to

tension, full tensile yield develops, but the sides remain in the elastic state. The stress

Moatsos, I. 2005


distribution in the vicinity of the neutral axis is linear. From the absence of net axial force

acting on the hull girder and the stress distribution in the vicinity of the neutral axis being

linear elastic, the neutral axis of the hull section at collapse is calculated. The ultimate

moment capacity is then obtained by integrating the first moment of the longitudinal

stresses with regard to the neutral axis. This approach was later extended to a general hull

section with multi-decks and multi-longitudinal bulkheads/side shell as shown in (Fig. 6.4).

The figure also shows the presumed longitudinal axial stress distribution over the hull

section at the ultimate limit state. The number of horizontal and vertical members is (m+ l)

and (n=l) respectively. The coordinate Y indicates the position of horizontal members (such

as bottoms and decks) above the base line and Zj shows the position of vertical members

(such as side shells and longitudinal bulkheads) from a reference (left/port) outer shell. The

sectional area of horizontal members at Y=Yi is denoted by Ay;, while the sectional area of

vertical members at Z =z; is denoted A;;j. In the sagging condition the longitudinal stress

distribution over the hull cross-section can be expressed as:

ax =aoB at y= Yo =0 (outer bottom)

1=-[(uusu +uosJy-HuosJ at 0::;; y::;; HH

= -uusu at H::;; Y ::;;D1

= --[(Uusu +aosJYi - HuoSL] at Y = Yi i = 1,2,... ,(m -1)H

= -uuD at Y = YJdeck)

(6.38)

Where subscripts Land U indicate the lower and upper parts of side shell plating,

respectively. No net axial force acts on the hull i.e.:

(6.39)

and the stress distribution in the vicinity of the neutral axis is elastic linear. The neutral axis

g above the base line may be calculated from

HUoSLg =---"=-ausu+aoSL

H = CID +~C12D2 + 2C2D

(6.40), (6.41)

Moatsos, I. 2005


Where

(6.42), (6.43)

The ultimate moment capacity of the hull for sagging is then given by

M Vus = -A)""O"UD(D- sl+ ~ (O"uSu+O"osLfL:~l A).;(gYi - yn]+

+O"osLfL:~l AYi(Yi - g )]- 2~ t~=oAlj XD- HXD+H - 2g )o-usu - AyoO"oBg- :v t~=oAlj )(6.44)

x [(2H -3gpuSu -(H -3gPosJ

Where g and H are calculated from (Eq. 6.40) and (Eq. 6.41) respectively.

Similarly in the Hogging condition, the stress distribution can be expressed as:

a, = O"oD at Y = Ym = 0 (Deck)1

= --[(O"USL + O"osu)Y - HO"osu] at 0 ~ Y ~ HH

= -O"uSl at H ~ Y ~ D

= _!_ [(O"USL+ O"Usu )Yi - H O"osu] at y = Yi' i = 2,3, ... , (m -1)H

= -O"uIB at Y = Yi (Inner Bottom)

= -O"uB at Y = Yo (Outer Bottom)

(6.45)

It is noted that, for simplicity, the positive direction of the y-axis in hogging condition is

taken opposite to that of sagging condition. The ultimate moment capacity of the hull under

Hogging is then obtained as:

Moatsos, I. 2005


g = HCfosu • H =C1D+~CI2D2 +2CzD,CfuSL +Cfosu

The approach suggested has a number of weaknesses and the quality of the results is

compromised as a result of the following factors:

1. The strength of each hull girder section (deck, bottom, etc) depends on the average

or weighted average of the ultimate strength of each element not taking into account

the position of each element or the behaviour of the surrounding elements.

2. Highly complex structures with internal bulkheads and multiple decks such as ro-ro

and passenger ferry vessels cannot be analysed since the complexity of the structure

and the interaction between multiple decks and bulkhead cannot be effectively

modelled with the set of assumptions taken by the method.

3. The method looks at the imposed stresses without taking into account the behaviourof the entire structure and the changes that occur in its longitudinal shape.

6.7.6. Modified Smith Analytical Approach

The alternative approach examined is that suggested by Gordo, Gudes Soares and Faulkner

(1996) which follows the general approach presented by BiIIingsley (1980) and by

Rutherford & Cadl well (1990) based on the original suggestions by Smith(1977). The

approach suggests that the moment curvature relationships is determined by imposing a set

of curvatures on the hull's girder. For each curvature the state of the average strain of each

beam column element is determined. Entering with these values in the load-shortening

Moatsos, 1. 2005


curves, the load sustained by each element may be calculated. The bending moment

sustained by the cross section is obtained from the summation of the moments of the forces

in the individual elements and the derived set of values defines the desired moment-

curvature relation.

The method makes a number of basic assumptions:

1. The elements into which the cross section is subdivided are considered to act and

behave independently.

2. Plane sections are assumed to remain plane when curvature is increasing; this

condition is necessary to estimate the strain level of elements, but its validity is

doubtful when shear is present in plane elements.

3. Overall grillage collapse is avoided by sufficiently strong transverse frames.

Initially the position of the neutral axis is required and is estimated though an elastic

analysis because, when the curvature is small, the section behaves elastically. The elastic

neutral axis passes through a point given by:

Gx = 0, due to symmetry

(6.47)

where Ai is the sectional area of element i, and Yi the distance of the centroid of element i to

the baseline and the origin is centred in the intersection of the baseline and centerline as it

can be seen in (Fig 6.5).

The most general case corresponds to that in which the ship is subjected to curvature in the

x- and y-directions, respectively denoted as C, and C; The Global curvature C is related to

these two components by:

(6.48)

or by:

Moatsos, I. 2005


C, = CcosBC, = CsinB

(6.49)

adopting the right hand rule, where B is the angle between the neutral axis and the x -axis.

The strain at the centroid of any element ti is consequently:

(6.50)

or from (Eq. 6.49):

e, = C(y gi cos B - X gi sin e) (6.51)

where (Xgi, Ygi) is the vector from the centroid of the section to the centroid of the element i

(stiffener and associated effective plate). The relation between these local coordinates and

the global coordinates is:

Xgi = Xi -Gx

Ygi = s, -o,(6.52)

(Eq. 6.50) and (Eq. 6.51) are still valid if one used any point belonging to the neutral axis

instead of the point on the intersection of the axes resulting from horizontal and vertical

equilibrium of the longitudinal forces due to the bending moment.

Once the strain state of each element is achieved, the corresponding average stresses are

then calculated and consequently the components of the bending moment at a curvature C

are:

M x = LY gi<l>~)o-oAi

My = LXgi<l>~)o-oAi(6.53)

where Xgi and Ygi are the distances from the element i to a local axis of a reference datum

located in the precise position of the instantaneous centre of gravity (CG) and e, is the

nondimensional strain of the element i at the instantaneous curvature.

Moatsos, I. 2005

Chapter 6. Ultimate Strength . 223

The modulus of the total amount is:

(6.54)

which is the bending moment on the cross section if the instantaneous CG is placed in the

correct location. Along the step-by-step process, however, this location shifts and so it is

necessary to calculate the shift between the two imposed curvatures. Rutherford and

Caldwell (1990) suggested that the shift could be taken equal to:

(6.55)

The expression seems to underestimate the shift and may cause problems in convergence.

As an alternative Gordo, Guedes Soares and Faulkner (1996) have proposed a trial and error

approach, having as stopping criteria, one of two conditions, the total net load in the section

NL or the error in the shift estimation LtGshould be less than or equal to sufficiently low

values:

NL= L(a;A;}$;;aoL(A;}

NL

(6.56)

AG = kE " $; 0.0001CE~A;(6.57)

(Eq. 6.56) and CEq.6.57) demonstrate the two conditions analytically, where; was taken

equal to 10,6. The factor kE is a function of the curvature and yield strain introduced to

permit a better convergence of the method, and it is a result of the variation in global

tangent modulus of the section with curvature.

However, the approach creates two distinct problems in its implementation:

1. The sequence and spacing of the imposed curvatures strongly influences the

convergence of the method due to the shift of the neutral axis.

Moatsos, I.2005


2. Modelling the ship's section and determining the position of the neutral axis itself

are important issues.

6.8 Comparative ResultsBased on the theories described in the previous sections, a comparative study was carried

out to determine the best approach for modelling the ultimate strength of stiffened panels

and the overall hull girder. A computer code in Visual Basic running in MS Excel 2003

called MUSACT (Moatsos Ultimate Strength Analysis with Corrosion and Thermal effects)

was written based on all the theories described in this chapter so far and the theories and

approaches in (Chapter 5), (Chapter 7) and (Chapter 8) of this thesis. MUSACT was made

to analyse and to compare the results obtained by the formulation and with all of the 3

FPSO vessels analysed.

The formulation and theoretical approaches explained in detail in previous sections of this

chapter are combined in the MUSACT to provide a comparative analysis of the different

approaches available for determining the overall ultimate strength of the hull girder but also

as a means of comparing the overall suggested approach that the MUSACT code uses but

also to form the basis upon the Thermal Stress analysis and the comparison of different

corrosion approaches will be compared and utilized by the code. Stress-strain data from

using the LR.PASS Program No. 20202 which calculates the strength strain relationship of

various types of different stiffened panels is also incorporated in the analysis providing the

basis for combining the modified Smith Analytical approach with the unstiffened and

stiffened plate analysis approaches by Guedes Soares (1988) and Faulkner (1975)

respectively. The code iteratively utilizes all stress strain relationships from a large database

of stiffened panels of various geometrical and material type configurations modeled for all

the FPSOs analyzed in this study and the theory extensively described in previous sections

of this chapter accordingly to converge to the correct solution as the curvature progressively

increases.

A sample window of the code is MS Excel 2003 can be seen in (Fig. 6.6) with (starting

clockwise from top right) the Panel Data Input window, the Corrosion Model Data window

and the Results & Reports window visible. In (Fig. 6.7) the VB Editor with part of the

MUSACT macro source code can be seen. As an example of the analysis carried out (Fig.

6.8), (Fig. 6.9) and (Fig. 6.10) illustrate the effect of the variety of formulation on the

Moatsos, I. 2005


average US of stiffened panels on the outer bottom, deck and side of the structure

respectively.

The effect of corrosion models will be discussed in detail in Chapter 7 but as it can be seen

from (Fig. 6.11) for sagging hull girder US and (Fig. 6.12) for hogging hull girder US

clearly when combined with the different US formulation, the results can vary and as it can

be seen from (Table 6.1) for Anasuria the difference is in the range of 3.4% for the OB,

7.5% for SS, 3.1% for the Deck, 2% for Sagging US and 1.5% for Hogging US for no

corrosion between the Paik simplified formulation plate US approach and the author

developed analytical approach with the Paik approach providing more conservative results.

In a similar fashion the results for Schiehallion can be seen in (Table 6.2) and for Triton in

(Table 6.3).

6.9 Validation against Commercial Code LRPASSThe suite of computer programs entitled LRPASS (Lloyd's Register, 1997) developed in

Lloyd's Register of Shipping (LR) was used to validate the results obtained by the

MUSACT code developed. In LRPASS local strength characteristics generated at specified

locations around the hull are used to evaluate the moment-curvature response. The

procedure used by LRPASS Program 20203 is based on the approach by Smith (1977) for

the overall hull girder. As a first step in the analysis, the selected cross-section of the hull is

subdivided into elements which are assumed to act independently. Two further assumptions

are made:

• Any stresses acting in the transverse direction have a negligible effect on the

elements' behaviour under longitudinal stress. This can be justified on the basis that

the panels between transverse frames are longitudinally stiffened only, thus

generating a stress field which is predominantly longitudinal.

• Any incompatibility of out-of-plane displacements between adjacent elements is

negligible. Again the typical design of stiffened panel between transverse frames

and deep girders in the main strength zones of deck and bottom involves panels

whose element sections and properties are uniform across the panel width, so that

relative displacements between adjacent elements will be small or zero.

Moatsos, I. 2005


For the ultimate strength of the stiffened panels a beam-column approach is used in which

the panel behaviour is typified by that of a single stiffener together with an effective width

of plating. The overall axial strength is obtained from a strut formulation in which the

individual plate and stiffener strengths provide the limiting extreme fibre stresses. The

original theory, developed by Chaterjee & Dowling (1977) for application to box-girder

bridges, has been modified according to Rutherford & Caldwell (1990), to allow for

moderate applications of lateral pressure in conjunction with axial stress and to take into

account stiffener buckling, according to Rogers (1975). Full details of this revised theory

which forms the LR.PASS Program No.20202 are given in (Rutherford, 1982) but also in

the appendix of the paper written by Rutherford & Caldwell (1990). Transverse stress in the

bottom structure resulting from pressure on the side shell have been estimated to be

approximately 4% of the yield stress for tanker type structures according to Rutherford &

Caldwell (1990). This level of stress will have a negligible influence on the axial-carrying

capacity of the structure and has therefore been ignored. Overall bending of the bottom

structure between bulkheads and girders has been similarly ignored on the basis that the

resulting longitudinal plating tension in the vicinity of these members will be counteracted

by compression in the remaining structure. Lateral pressure effects on a local level

considered in the analysis are therefore restricted to:

• Local bending of plate panels between stiffeners

• Overall bending of the stiffened panels between frames.

Both of these are accounted for automatically in the theory used to generate element stress-

strain data. Two predictions of ultimate strength of stiffened plate elements are given by the

program:

• One relating to plate induced failure

• One relating to stiffener induced failure.

The lowest of these defines the ultimate condition and identifies the mode to be used in

selecting a load shedding response beyond the ultimate stress. In this respect, four separate

theories are includes in the program, two for plate failure and two for stiffener failure; in

both cases, one theory allows for buckling while the other assumes pure plastic action. The

Moatsos, I.2005


buckling theories follow the work of Murray (1973) and are described together with the

plastic theories in Rutherford (1982). The stiffener buckling theory relates strictly to flat bar

stiffeners and consequently the plastic theory is used for angle and tee sections. The theory

can be found summarised in Rutherford & Caldwell (1990). The results using LRPASS for

the overall hull girder ultimate strength of the 2 FPSOs analysed when curvature is applied

on the structure can be seen in (Fig. 6.13) for sample output of the LR.PASS Program

No.20202 stress-strain relationships generated code for one of the stiffened panels from the

Triton FPSO analysed, (Fig. 6.14) and (Fig. 6.15) for the Triton FPSO in sagging and

hogging respectively, (Fig. 6.16) and (Fig. 6.17) for the Schiehallion FPSO for sagging and

hogging respectively and (Fig. 6.18) and (6.19) for the Anassuria FPSO for sagging and

hogging respectively. The ultimate bending moment results can be seen in summarised form

in (Table 6.4). A comparative graph showing results from both LRPASS and MUSACT can

be seen in (Fig. 6.20) for Anassuria FPSO, (Fig. 6.21) for Triton and (Fig. 6.22) for

Schiehallion FPSO analysed with the results obtained using the MUSACT code proving to

be of a similar magnitude to the results obtained from LRPASS until the ultimate bending

moment is reached but varying significantly in the post ultimate region. A comparative

graph of the results obtained from all 3 FPSOs comparing the ultimate bending moment in

sagging and hogging conditions can be seen in (Fig. 6.23)

6.10 Validation against Experimental DataIn the available published literature six large scale box girder test models were found which

were tested under pure vertical bending. Results of the test and the model sections have

been published in Dowling, Moolani and Frieze (1976), Nishhara (1983) Mansour, Yang

and Thayamballi (1990) and Dow (1991) can be seen in Figures 5-8. Dowling's models

were originally tested in the sagging condition, but since the compression flanges were

heavier than the tension flanges, the actual situation corresponds to a hogging condition if

the model is turned over. Dowling, Moolani and Frieze (1976) provided experimental data

of the ultimate strength of the compression flanges as well as of the overall hull. In

Mansour's Test model II under the hogging condition, the bending moment was generated

using air pressure cells (positive or negative pressure) located below the model, idealizing

bottom pressure and load distribution on actual ship hulls. The other models were all loaded

by a four-point bending mechanism. Experimental data for a larger model that can reduce

scaling effects is always preferable when attempting to check the validity of simplified

methods. Taking this into account the best model in the published literature is the one

Moatsos, I.2005


reported by Dow (1991) who tested a one-third-scale frigate hull model in the sagging

condition.

As our theoretical model was decided after comparison of some of the available options,

although each one of the methods has been compared against some form of full scale data,

test measurements or FEA analysis, it would be interesting to investigate how well our

developed code and approach compared against some of the published test data available in

the relevant literature in order for us to ensure that the approach is providing accurate results

for use in reliability analysis. In the available literature, 6 large-scale box girder test models

under pure vertical bending as shown in (Fig. 6.24a-c) from Dowling, Moolani & Frieze

(1976), (Fig. 6.25a-b) from Nishihara (1983), (Fig. 6.26) from Mansour, Yand and

Thayamba1li (1991) and (Fig. 6.27) from Dow (1991). A Comparative study between the

scale model tests and results using the MUSACT code was carried out to ensure the validity

of the calculated figures that will be used for reliability analysis.

In (Table 6.5) the comparison between the experimental values available in the published

literature, the MUSACT code using the modified Smith (1977) approach and the combined

Paik & Mansour (200 1) and Paik & Thaymaballi (1997) approach but also ALPSIISUM

results available in Paik & Mansour (1995). For calculation of the hull girder ultimate

strength using the Paik & Mansour (200 1) approach, the designer needs to know in advance

the ultimate strength of the compression flange as well as the sides in the vicinity of the

compression flange and that is the reason behind using the Paik & Thayamballi (1997)

approach. The ultimate strengths of the compression flange for all test model sections are

shown in the first part of (Table 6.5) and by comparison with the results of Dowling's

models it was found that the Paik & Thayamballi (1997) approach provides a reasonable

solution with an error of 15% in the worst case.

There are significant differences in the results as the last columns in the table show the

percentage error of the formulation when compared with the experimental results. As seen

in the second section of (Table 6.5) the proposed approach gives a closer agreement with

the experimental and numerical results. It could be said that the differences between the

combined approach and the MUSACT could be a results from the difference in stress

distribution in the sides. In the combined formulation, the stresses are assumed to remain in

the elastic range for the areas of the sides under compression in the immediate vicinity of

Moatsos, 1. 2005


the final neutral axis as well as for the areas under tension. The MUSACT codes does not

make this assumption but instead utilises the moment curvature relationships as described in

the relevant section of this chapter.

6.11 Discussion-ConclusionsFor the closed form formulation used credible distributions of longitudinal stresses over the

hull section at the overall collapse state were assumed and it was postulated that part of the

compressed side shell as well as the compression flange will reach their ultimate limit state

in compression. The tension flange will reach the yield strength of the material while

compressed side shells in the immediate vicinity of the final neutral axis as well as all side

shells under tension are assumed to remain elastic and the stress distribution there is

assumed to be linear. The neutral axis location as well as the depth at which the stress

distribution starts to become linear can be determined from two conditions:

1. No axial force exists on the hull girder.

2. The stress distribution is linear near the neutral axis.

The approach calculates the ultimate strength moment of the hull by integrating the assumed

stress distribution with respect to the neutral axis. This resulted in explicit ultimate moment

expressions for the sagging and hogging conditions. The simplified formulation assumed

uniform compressive stress distribution (average values), but the actual stress distribution

will be non-uniform as a result of buckling and post buckling effective width. If the uniform

value is a good indication of the actual value, then the calculated moment should not be

very different from that due to the actual stress distribution, because the distance to the

neutral axis is the same in both cases. As the emphasis of the approach is to use simple

formulation, uniform (average) compressive stress is assumed.

As far as the developed code that formed the core part of the MUSACT code is concerned

and the theory behind this approach the bending moment sustained by the cross section is

obtained from the summation of the moments of the forces in the individual elements and

the derived set of values defines the desired moment-curvature relation. The method makes

a number of basic assumptions than need to be stated:

Moatsos, I. 2005


1. The elements into which the cross section is subdivided are considered to act and

behave independently.2. Plane sections are assumed to remain plane when curvature is increasing; this

condition is necessary to estimate the strain level of elements, but its validity is

doubtful when shear is present in plane elements.3. Overall grillage collapse is avoided by sufficiently strong transverse frames.

Moatsos, I. 2005


Chapter 6, Reference:

Beghin, D., Jastrzebski, T., Taczala, M. 1995, "Result- A Computer Code for Evaluation ofthe Ultimate Strength of the Hull Girder", Proceedings of the International Symposiumof Practical Design of Ships PRADS95, Seoul, Korea, September, pp 832-843.

Billingsley, D.W. 1980, "Hull Girder Response to Extreme Bending Moments",Proceedings of the 5th STAR Symposium, The Society of Naval Architects and MarineEngineers (SNAME), pp 51-63.

Bonello, M.A., Chryssanthopoulos, M.K., Dowling, P.J. 1991, "Probabilistic StrengthModelling of Unstiffened Plates under Axial Compression", Proceedings of the Jd

h

International Conference on Offshore Mechanics and Arctic Engineering (OMAE91),Stavanger, Norway, June 1991.

Bonello, M.A., Chryssanthopoulos, M.K. 1993, "Buckling Analysis of Plated StructuresUsing System Reliability Concepts", Proceedings of the tr" Offshore Mechanics andArctic Engineering Conference (OMAE93), Glasgow Scotland, UK, Vol. 2, pp 313-321.

Caldwell, J.B. 1965, "Ultimate Longitudinal Strength", Transactions of the Royal Institutionof Naval Architect (RJNA), Vol. 107, pp 411-430.

Carlsen, C.A., 1977, "Simplified Collapse Analysis of Stiffened Plates", NorwegianMaritime Research, No.4.

Carlsen, C.A. 1980, "A Parametric Study of Collapse of Stiffened Plates in Compression",The Structural Engineer, Vol. 58b, No.2, June 1980.

Chalmers, D.W., Smith, C.S. 1992, "The Ultimate Longitudinal Strength of a Ship's Hull",Proceedings of the 5th International Symposium on the Practical Design of Ships andMobile Units (PRADS '92), University of Newcastle Upon Tyne, UK.

Chaterjee, S., Dowling, P.J. 1977. "The Design of Box Girder Compression Flanges", SteelPlated Structures, Dowling, PJ. (Ed), Crosby Lockwood Staples, London.

Das, P.K. 2004, "Analysis and Design of Stiffened and Unstiffened Plates" Notes fromASRANet Course Design by Advanced Structural Analysis, ASRANet, Glasgow,Scotland, UK, May 2004. .

Det Norske Veritas, 2004, DNV Rules for Ships, Rules for Classification, 1, Pt. , Ch. 1,Sec.5, pp 39-60.

Dow, R.S. 1991, "Testing and Analysis of a 1/3-Scale Welded Steel Frigate Model",Proceedings of the International Congress on Advances in Marine Structures, Elsevier,London-New York, pp 749-773.

Dowling, P.J., Molani, P.M., Frieze, P.A. 1976, "The Effect of Shear Lag on the UltimateStrength of Box Girders", International Congress on Steel Plated Structures, ImperialCollege, London, July, pp 108-147.

Evans, J.H. (Ed), 1975, Ship Structural Design Concepts, Cornell Maritime Press.Faulkner, D. 1975, "Compression Strength of Welded Grillages", Chapter 21 in Ship

Structural Design Concepts, Edited by Evans, J.H., Cornell Maritime Press, pp 633-712.

Faulkner, D. 1975, "A Review of Effective Steel Plating for Use in the Analysis ofStiffened Plating", Journal of Ship Research, Vol. 10. pp 1-17.

Moatsos, I. 2005


Faulkner, D. 1977, "Compression Tests on Welded Eccentrically Stiffened Plates used inGirders", Steel Plates Structures, PJ. Dowling et al, (Eds), Crosby Lockwood Staples,London, pp 581-617.

Faulkner, D., Sadden, J.A. 1979, "Toward a Unified Approach to Ship Structural Safety",Transactions of the Royal Institution of Naval Architects (RINA), Vol. 121, pp 1-28.

Faulkner, J.A., Clarke, J.D, Smith, C.S., Faulkner, D. 1984, "The Loss of HMS Cobra-aReassessment", Transactions of the Royal Institution of Naval Architects (RINA), Vol.126, pp 125-151.

Frieze, P.A. et al. 1991, "Report of Committee V.1. Applied Design", Proceedings of the1J'h International Ship and Offshore Structure Congress, Hsu, P.H. & Wu Y.S. (Eds),Elsevier Applied Science, London.

Frieze, P.A., Lin, Y.T. 1991, "Ship Longitudinal Strength Modelling for ReliabilityAnalysis", Proceedings of the Marine Structural Inspection, Maintenance andMonitoring Symposium, SSC/SNAME, Arlington, Virginia, March, 111.B.l-111.B.19.

Goodman, L.E., Rosenblueth, E., "Newmark, N.M., 1954, "Aseismic Design of FirmlyFounded Elastic Structures", ASCE Transactions, Proceedings Paper 2726.

Gordo, J.M., Guedes Soares, C. 1993, "Approximate Load Shortening Curves for StiffenedPlates Under Uni-axial Compression", Integrity of Offshore Structures-S, D. Faulkner etal. (Eds), EMAS, pp 189-211.

Gordo, J.M., Guedes Soares, C., Faulkner, D. 1996, "Approximate Assessment of theLongitudinal Strength of the Hull Girder", Journal of Ship Research, Vol. 40, No.1, pp60-69.

Guedes Soares, C. 1988, "Design Equation for the Compressive Strength of UnstiffenedPlate Elements with Initial Imperfections", Journal of Constructional Steel Research,Vol. 9, No.4, pp 287-310.

Home, M.R, Narayan, R. 1976, "Ultimate capacity of stiffened plates used in girders",Proceedings of the Institute of Civil Engineers, Vol. 61, Part 2, pp 253-280.

Home, M.R, Monatgues, P., Narayan, R 1977, "Influence on Strength of CompressionPanels of Stiffener Section, Spacing, and Welded Connection", Proceedings of theInstitute of Civil Engineers, Vol. 63, Part 2, pp 1-20.

lACS 1989, lACS Requirement S7, Minimum Longitudinal Strength Standards, Revision 3,International Association of Classification Societies, London, United Kingdom.

lACS 2003, lACS Requirement Sl l, Longitudinal Strength Standard, Revision 3",International Association of Classification Societies, London, United Kingdom.

ISSC 2000, "Ultimate Strength", Committee 111.1Report, Proceedings of the InternationalShip Structures Congress 2000, Vol. 1, Nagasaki, Japan, Elsevier, pp 257-308.

ISSC 2000, "Ultimate Hull Girder Strength", Committee VI.2 Report, Proceedings of theInternational Ship Structures Congress 2000, Vol. 2, Nagasaki, Japan, Elsevier, pp 321-390.

ISSC 2003, "Ultimate Strength", Committee 111.1Report, Proceedings of the InternationalShip Structures Congress 2000, Vol. 1, San Diego, USA, Elsevier.

Moatsos, I. 2005


Kutt, L.M., Piaszczyk, C.M., Chen, Y.K., Lin, D. 1985, "Evaluation of the LongitudinalUltimate Strength of Various Ship Hull Configurations", Transactions of the Society ofNaval Architects and Marine Engineers (SNAME), Vol. 93, pp 33-53.

Lin, Y.T. 1985, "Ship Longitudinal Strength Modelling", PhD Thesis, Department of NavalArchitecture and Ocean Engineering, University of Glasgow, Glasgow, Scotland.

Lloyd's Register of Shipping. 1997, LR.PASS Personal Computer Programs, User'sManual, Vol. 2 Direct Calculations, London, England, UK.

Lloyd's Register of Shipping. 1997, LR.PASS Personal Computer Programs, User'sManual, Vol. 3 Ship Initial Design, London, England, UK.

Mansour, A.E., Faulkner, D. 1973, "On Applying the Statistical Approach to Extreme SeaLoads and Ship Hull Strength", Transactions of the Royal Institution of Naval Architects(RINA), Vol. 115, pp 277-313.

Mansour, A.E., Yang, J.M., Thayamballi, A. 1990, "An Experimental Investigation on ShipHull Ultimate Strength", Transactions of the Society of Naval Architects and MarineEngineers (SNAME), Vol. 98, pp 411-440.

Mansour, A.E., Lin, Y.H., Paik, J.K. 1995, "Ultimate Strength of Ships under CombinedVertical and Horizontal Moments" Proceedings of the International Symposium onPractical Design of Ships and Mobile Units (PRADS95), Seoul, Korea, Vol. 2, pp 985-990.

Mansour, A.E., Wirsching, P.H., Lucket, M.D., Plumpton, A.M., Lin, Y.H. 1997,"Structural Safety of Ships", Transactions of the Society of Naval Architects and MarineEngineers (SNAME), Vol. 105, pp 61-98.

Murray, N.W. 1973, "Buckling of Stiffened Panels Loaded Axially and in Bending", TheStructural Engineer, Journal of the Institute of Structural Engineers, London, UK.

Niho, o. 1978, "Ultimate Strength of Plated Structures", PhD Thesis, Department of NavalArchitecture and Ocean Engineering, University of Tokyo, Tokyo, Japan (In Japanese).

Nishihara, S. 1983, "Analysis of Ultimate Strength of Stiffened Rectangular Plate", (inJapanese), Journal of the Society of Naval Architects of Japan, Vol. 154, pp 367-375.

Paik, J.K., Mansour, A.E. 1995, "A Simple Formulation for Predicting the UltimateStrength of Ships", Journal of Marine Science and Technology, Vol. 1, December, pp52-62.

Paik, J.K., Thayamballi, A.K. 1997, "An Empirical Formulation for Predicting the UltimateCompressive Strength of Stiffened Panels", Proceedings of the 1h International Offshoreand Polar Engineering Conference (ISOPE97), Honolulu, Hawaii, USA, 25-30 May.

Paik, J.K., Hughes, O.F., Mansour, A.E 2001, "Advanced Closed Form Ultimate StrengthFormulation for Ships", Journal of Ship Research, Vol. 45, No.2, June, pp 111-132.

Pu, Y., Das, P.K. 1994, "Ultimate Strength and Reliability Analysis of Stiffened Plate",Dept. of Naval Architecture and Ocean Engineering Report NAOE-94-37, University ofGlasgow, Scotland, UK.

Rhodes, J. 1981, "On the Approximate Prediction of Elasto-Plastic Plate Behaviour",Proceedings of the Institute of Civil Engineers, London, UK, Vol. 71, pp 3-12.

Rogers, N.A. 1975, "Outstand Failure in Stiffened Steel Compression Panels", CambridgeUniversity Report, CUED/C-StructffR.54.

Moatsos, I. 2005


Rutherford, S.E. 1982, "Stiffened Compression Panels: the Analytical Approach", Lloyd'sRegister Internal Report, No.82/261R2.

Rutherford, S.E., Caldwell, J.B. 1990, "Ultimate Longitudinal Strength of Ships, A CaseStudy", Transactions of the Society of Naval Architects and Marine Engineers(SNAME), Vol. 98, pp 441-471.

Shi, W.B. 1992, "In Service Assessment of Ship Structures: Effects of General Corrosion onUltimate Strength", Presented at the Spring Meeting of the Royal Institution of NavalArchitects (RINA), No.4.

Smith, C. 1977, "Influence of Local Compressive Failure on Ultimate Longitudinal Strengthof a Ship'S Hull", Proceedings of the International Symposium on Practical Design inShipbuilding (PRADS77), Tokyo, Japan, pp 73-79.

Smith, C.S. 1983, "Structural Redundancy and Damage Tolerance in Rleation to UltimateShip-Hull Strength", Proceedings of an International Symposium on The Role of Design,Inspection and Redundancy in Marine Structural Reliability, US National ResearchCouncil, National Academy Press, Washington DC, pp 91-117.

Smith, C.S., Anderson, N., Chapman, J.c., Davidson, P.C., Dowling, P.J. 1991, "Strength ofStiffened Plating under Combined Compression and Lateral Pressure", RINA SpringMeeting Paper No.4, London, UK.

Valsgaard, S., Steen, E. 1991, "Ultimate Hull Girder Strength Margins in Present ClassRequirements", Proceedings of the Marine Structural Inspection, Maintenance andMonitoring Symposium, SSC/SNAME, Arlington, Virginia, March, 111.B.l-111.B.19.

Vasta, J. 1958, "Lessons Learned from Full Scale Structural Tests", Transactions of theSociety of Naval Architects and Marine Engineers (SNAME), Vol. 66, pp 165-243.

Vilnay, 0., Rockley, K.C. 1981, "A Generalised Effective Width Method for Plates Loadedin Compression", Journal of Constructional Steel Research, Vol. 1, No.3, pp 3-12.

Viner, A.C. 1986, "Development of Ship Strength Formulations", Proceedings of theInternational Conference on Advances in Marine Structures, Elsevier, London, pp 152-173.

Wickham, A.H.S., Hart, D.K. 1983, "A Review of Structural Uncertainties", Lloyd'sRegister of Shipping, Internal Report No.84/22.

Yao, T. 1980, "Ultimate Compressive Strength of Ship Platings", PhD Thesis, Departmentof Naval Architecture and Ocean Engineering, University of Tokyo, Tokyo, Japan (InJapanese).

Moatsos, I.2005


Appendix 6, Figures

p

7

/,~--------- A ~,--------~~

t PLATE THICKNESSp LONGITUOINALS

q TRANSVERSES

Figure 6.1 Stiffened plate definitions (Faulkner 1972)

AD

As-

t

Figure 6.2 Equivalent section configuration of a ship's hull

Figure 6.3 Linear Distribution of longitudinal axial stresses in a hull section

Moatsos, I. 2005


v:.711VinVlVo

Zo Z1 Zf Zj Zn·f Zn·1 Zn

The HullSeetion

Figure 6.4 Presumed longitudinal stress distribution over hull cross section at overall collapse state

Figure 6.5 Combined bending of the hull girder

~~- ,_,_ .~..... ~~ ..... ~.- --- - - - - ~~A..~ .......- u ~~.~. ....... -..~~ -. . .~. 1oQf'I..'......" - "'ft,t-~ ·_M - .- - .- wt•. '~ •.. _n _.- - ~ "'" .._. _ . .~....."-~ _. ..-_. _, t,.Ul.~_. - _.-.. ._, -..~ UA - _A -_u~ " .- -....:~7'~'.~...-

~__ ... u ..

• ..... , -.u'~", ,,..,

.. ~~~E~': L~• .1'IA »1,.,. •. _,._

...... rwrN .._H. __• .w. uoa.fM"'_ ~_'!: ::: :::::::::

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'~~"_I"_fy,_' lK","_ rt._,,..al Hol:ttt tt.tl'M I''''

~§§'~~:§.!.: '!.': ::: :.:

1< ) I

Ct.. •

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'.NI... .... NI_.f "NI

'.NI

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,~..~.--...~.n.•It.'tu ..NI ~._

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"._. IU_. tU 1M.. tU J.'"'.t .... I... ,...,... ,... tfrM... ... ... ... I.. ..,....

r'IJ:i¥, 'dl.·~:ti ~O.'_:f.:»-J't .:....1"

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.- un. ~ .- .~..~ ..,_ .- un 'M' u•:::: ..- .-._'"" ..- .- ..~ ... '.N • UN ..- •.U, .~k_ .MM ~ ..- ..- .- .M un ..- u. U1' ..- ....., ."

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._~ I.'" .~,,_ ..~ .~_. u. ...un .~,,.*.... .... ~ ..- ..- ..- 'GO u~ .~.- UN

IA.IOIIOI) .- '.'Il ,~ ..~ L~ L~

:-!" ._U~ ..- '.nl .... ,~ .- .~...~ ._. ,•. UM UII .n. ~ ..- .~-~ ~ ... .., ..."."""" U~ .~. ..- .., LM' !."' ... .~

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""..., ._= ..- ..,n '.-

v,,-_.

"~~A~erB L~"Z~iS:; i~1R~:Z;~?O.. . .

Figure 6.6 MUSACT VB Code for MS Excel 2003.

Moatsos, I. 200S


tl Microsoft V;. ... ,lIasic . AnassurUS.xls - [Modulel ((ode)),4 E" ~.. _ lr-' _ Qebuo &.., 1oo1s add-lns ~ t!oI?

H~j·'d 1 I>" "~I~_j":; I ..dI,Geneul1

+ luncre:s (FI.KRES.XUI ...+ .. Intemet_Auiltant (t

-~_je<t(""""'1- es Micr050ft Excel Ob;ec

@) Sheet, (Word.@)_'O(_,@JSheet2 (0<.<"")@) Shoot3 (lmri)@) Shoot. (Sklc)@) Shoot5(Oed<)@J_._)il"lSh8ItllRed:sl ..,

< 1 >

F'"Table Fa6sekn.--- 0- __R_

(SPPA(y) I 5hee'to("VPandLoad:!l") .ce i re t s , 3)) , (Shee't:!l("VPandLoeull5") .CelU(6, J) - lRHog('L ..(9PP1(y) 11 ARHog(y, 1) I (3 1 Sheet.!I("VPl!lnd.Loa~").Cel1s(6, 3)11· «2 1r AlUlog(y, 1) - 3

Sheets("Result.s") .ce i is (6 + y, 3) - 2 • lRHoq(y. 3) I 10 ,.. 9

''''.1r.Soaro!!~ Garbatov ccc roe rcn-Peax St. Panel

I saO'~1nQ1.RSsq(y, 6) _ (DGPA(y) 11 DGPUS(y) + 2 • 3GPl.(y) 11 5GPUS(y) - OBGP1.(y) 11' OBSY - IBGPl(y) " SST)

ARSaq(y, 7) ,. IBGP1(y) 11 Sheets ("VPandLoad!5'If) .ce i iets, 6) / SGP1(y)ARSl1q(y, 8) _ (ARSaq(y, 6) It 5heet.s('"VPanciLoad:!!llt) .Cells(6, 3) + Sqr( (ARSaq(y, 6) .. 2) .. (3hc:et......J.l.P.S~(y, 9) .. (.lP.Sao-(Y, 6) .. Shl!ets("VPandLoad.!l") .Cells(6, 3) + 3qr( (~ag(v, 6) .. 2) .. (SheetJ.RSao(y, 10) .. -DGPJ,(y) .. (Shee:t:!l("'VPandLoad:!!l").Ce:ll:!!l16, 3) - lR5aq(v. 51) .. DGPUS(?) - (SGPll

(IBGPJ.(y) / llSag(y, 8))" (lRSag(y, 9) _SheeU(WVPandLoads").Cell:!l16, 6»" (Sht!ees("VP@(SGP1(v) .. J.RSag(v, 8) I (3 .. Sheets("VPandLoad!l").Ce11:!!1(6, 3») .. (2" AR5aq(y, 8) - 3 '

Sheet:l("Rt!:!u.les") .Ct!1l:5(6 + y, S) .. Z .. USag(?, 10) / 10 ... 9

, Hoq~l.ngAIUkH~'(Y, 4) .. 9he:ets('"VPandLoads") .Cells(6, 3) .. (OBGPJ.(y) .. OBGPUS(y) ... IBGPA(V) .. IBG-PUS(y)UUIoq(y, 5) .. Sheets ('"VPandLoads") .ce i re t s, 3) .. (OBGP.l(V) .. OBGPtJS(y) .. SST + IBGPJ,(y) .. IBGI.t.RHog(y, 6) .. DGPAly) .. J.RBoq(y, S) .. DSY + OBGPA(y) .. (Sheee:!l('"VPMdLO&~") .Cell:!l(6, 3) - ARl

lElGPA.(y) .. (Sheets("VPand.Load.~") .Cells(6, 3) - J.RHog(y, SI - Shet!ts("VPandLoads") .Ce11:5(6,(SGPJ.(y) I Sheets ("VPandLoa&") .Ce11s(6, 3)1 .. (Shee:t:!l("'VPanclLoads") .Ce11:1(6, 3) - lRHog(\(SGPJ.(y) .. AlUIoq(y, 4) I (3" SheetSC"VPandLoad!l").Ce11::5(6, 3))) .. «(2 .. lRHog(y, 4) - 3 '

Shll!et::5C"Re:sules") .Ce:1h(6 ... y, 9) ,. 2 .. l..RHog(y, 6) I 10 A 9

' ....... Palk Coccosion-raulkner Se.Panel, 3agr;11n'J

UtSag(?, 11) • (DPP.1.(y) ... DPFUS(y) + 2 ... SPP.1.(y) ... SPFUS(y) - OBPP.1(y) ... OBSY - lBPPA(?) .. SS,

ARSag(y, 12) - lBPPA.(?) .. Sheec.:!!('"VPandLoads") .Cell:!l(6, 6) I SPPA(y)J.P,Saq(?, 13) _ (J.RSaq(y, 11) • Sheees('"VPandLoo.ds") .Celh(6, 3) + Sqr«lRSa~{?# 11) A 2) .. (St_;

10 20 25

Figure 6.7 MUSACT VB Code for MS Excel2003 Source Code

Effect of Corrosion and Strength Models in Outer Bottom PanelA\erage US--------------------------------------~~~_GPUS

J. PFUS

-x-GFUS

284282

€ 280~-- 278(/)::la; 276c~ 274 ----272

2700 5 3015

Time (Years)

Figure 6.8 Effect of various US formulation on OB stiffened panel average US (Anassuria FPSO).

Moatsos, I. 2005


205200

........ 195'EE~ 190UJ~ 185Qjc:~ 180

175170

0

Effect of Corrosion and Strength Models in Side Shell PanelA\erage US

-+-PR..E___ GFUS

PFUS

~GFLS

15Time (Years)

Figure 6.9 Effect of various US formulation on SS stiffened panel average US (Anassuria FPSO).

25 30

Effect of Corrosion and Strength Models in Deck Panel AwrageUS

268266264

~ 262E 260~t/) 258~Qj 256c:~ 254

252250248

0

5 10 20

-+-PR..E___ GFUS

- PFUS~GFUS

5 10 15Time (Years)

20 25 30

Figure 6.10 Effect of various US formulation on deck stiffened panel average US (Anassuria FPSO).

Moatsos, I.2005


-14000

-14500

-15000 /~

E/ ..

Z/ .....

:IE -15500 r_.. _/'en:::>

_.- -+- Paik Cor.lPaik St.Rate/

.>

-16000 ____ Paik Cor.lFaulkner SI.Rate

-16500Soares-Garbatov Cor.lPaiSI.Rate

~ Soares-Garbatov

-17000Cor.lFaulkner SI.Rate

0 5 10 15 20 25 30Time (Years)

Effect of Corrosion & Plate Strength Models in Sagging US

Figure 6.11 Effects of various corrosion and US formulation on hogging hull girder US (AnassuriaFPSO).

16000

15500

15000

14500 -

Effect of Corrosion & Plate Strength Models in Hogging US

____ Paik Cor.lFaulkner SI.Rate

Soares-Garbatov Cor .IPaikSI.Rate

~ Soares-GarbatovCor.lFaulkner SI.Rate

14000+---~----~----~----~--~~--~o 5 10 15 20 25 30

Time (Years)


Moatsos, 1. 2005


TruTON FPSO OT OCSCP 6 ; 450Xl1.5X15OXlI.l 1 AHJ2 19.5 OHJ2STRESS-STRAINCURVE Yield Stress = 315.00 Njmm2

Yield Strcin = 1529'E-{)J

STRAtI RATIO

Figure 6.13 Sample Stress-Strain Curve output from LRPASS for Triton FPSO.

o

TRITON FPSO OTOC HOGVERTICAl Wl.£NT -{;URVATURE GRAPH : SAGGING

xr-9

MAX = 7.1630E+12

200 250

VERTICAl. CURV-.TURE (mrn-1)

Figure 6.14 Triton FPSO Sagging US using LRPASS.

Moatsos, I.2005


--------------------------------------------------------------------TRITON FPSO otoc HOGVERTICAL MJl.£NT -CURVATURE GRAPH : HOGGING MAX = 9.7546E+12

1:$0IE-II

. VERTICAL CURV ....TURE (mm-1)

Figure 6.15 Triton FPSO Hogging US using LRPASS.

1)0

Sctiehollion FPSO or OC Ultim. StrengthVERTICAl ~NT -CURVATURE GRAP~ : SAGGING MAX = 1.4625E+13

Figure 6.16 Schiehallion FPSO Sagging US using LRPASS.VERTICJ\I.. CURV ....TURE mm-l

Moatsos, I. 2005


'.Sctiehallion FPSO OT OC Ultim. StrengthVERTICAL W£NT -CURVATURE GRAPI-f : HOGGING MAX = 1.6767E+13

VERTICAl. CURV....TURE(~_]

Figure 6.17 Schiehallion FPSO Hogging US using LRPASS.

---------------------------------------------------------------_.ANASSURIA FPSO OCOT SAGVERTICAl W£NT -CURVATURE GRAPH: SAGGING MAX = 1.0088E+13

xE12 VERTICAl.. Io4OIoEHT ("mm)

200"llO

VERTICAl CURVATURE mm-l

Figure 6.18 Anassuria FPSO Sagging US using LRPASS.

Moatsos, I. 2005


ANASSURIA FPSO OCOT HOGVERTICAL ~NT -CURVATURE GRAPH HOGGING WJ( = 1.1472E+13

3.0E-071.56+13

1.06+13

5.06+-12

O.OEtOO

-5.06+12

-1.06+13

-1.56+13

IE12 VERTICAl t.tOt.£NT (Nmm)12

50 100 150 200IE-9

VERTICAL CURVATURE (nvn-1'

Figure 6.19 Anassuria FPSO Hogging US using LRPASS.

LRPASS-MUSACT Ultimate Bending Moment Comparison ANASSURIA

-3.0E-07 O.OEtOO 2.0E-07-1.0E-07 1.0E-07-2.0E-07

EEz

Vertical Curvature (x1Q"9mm")

1_ M..JSAGr SAG - LAPASS SAG • LFPASS I-OG - M..JSACT I-OG 1Figure 6.20 LRPASS-MUSACT Validation of US Vertical Moment Results

Moatsos, I. 2005


LRPASS-MUSACT Ultimate Bending Moment Comparison TRITON

-3.0&07 -2.0&07 -1.0&07 0.06+00 1.0E-07 2.0E-07 3.0E-07

1.2&13

1.0&13

8.0&12

6.0&12

4.0&12

2.0&12

0.06+00

-2.0&12

-4.0&12

-6.0&12

-8.0&12

-1.0&13

Figure 6.21 LRPASS-MUSACT Validation of US Vertical Moment Results, (Triton FPSO).

-2.0&07 -1.5&07 -1.0&07 -5.0&08 0.06+00 5.0&08 1.0&07 1.5E-07 2.0E-07 2.5E-07

2.0E+13

Vertical Curvature (x1<t8mm-')

1- M..SACT SAG - LRPASS SAG ..... LAPASS I-()G _ M..SACT I-()G 1

LRPASS-MUSACT Ultimate Bending Moment ComparisonSCHIEHALLION

1.5E+13

1.0&13

5.0E+12

0.06+00

-5.0E+12

-1.0E+13

-1.5E+13

-2.0&13

Figure 6.22 LRPASS-MUSACT Validation of US Vertical Moment Results, (Schiehallion FPSO).

Vertical Curvature (x104 mm-')

1-M.BACT SAG - LFPASS SAG . LFPASS I-()G - M.BACT I-()G I

Moatsos, I. 2005


MUSACT Ultimate Bending Moment Comparison 3FPSOs Analysed

-3.013-07 -2.013-07 -1.013-07 0.06+00 1.013-07 2.013-07 3.013-07

2.0&13

1.5&13

1.0&13

5.0&12

0.06+00

-5.0&12

-1.0&13

-1.5&13

-2.0&13

Figure 6.24a-c Midhsip Sections of Dowling's box girder models tested in the hogging condition (mm)

Moatsos, 1. 2005

Vertical Curvature (x10" mm"]

- TRTON SAG - TRTON I-(JG AN<\SSLfllA SAG

-- AN<\SSLflIA I-(JG _ SOi8-V\LLION SAG - SQ-lI8-V\LLION I-OG

Figure 6.23 Comparative MUSACT results for all FPSOs analysed.

I - 157.4.8 ! = 157'.48

f---1219.2~ f---1219. 2___!._____..j

(b) Model"

, = 523.94

T-914.4

112.70 6.1468

69.85x79375Plat

1-----1219.2----..,

(c) "odel ]0


(..) Model KST-S (I» "'odel KST-~

Figure 6.25a, b Midship sections of Nishihara's box girder models tested in the sagging condition (mm)

L=609.6

t-r304.8-1T t (1) Zd2 ~(1) .508 9.525- - _L

17 : 2.7688(1) 50.8x9.525 Flat~ 63.5)(6.35Flate 31. 75x3.175 Flat

.!E ~ ~ 0l a> °1-------- 2438.4---------1

Figure 6.26 Midship section of Mansour's box girder model n tested in the hogging condition (mm)

1------ 2051) ---...;

base line

(unit. : mm)(f) 101.7)(3~ 203.2x3Q 203.2x2@ 38.1xl.78 ~W)

14,73)(3,3 F)~ 228.6';.3 Vi)

152.4X5 (F)® 162.0)(2 (W)

51.0"2 (F)e 117.5x2 (W)51.0x2 (F)

Q;b " 1.0x2 (W)5f.OX2 (Fj

~ 292.0'><6~ 120.0><6e 60.0)(.8~ 114.0><5 (W)

44.5)(9.5 (F)

Frame Spacing=457.2

Figure 6.27 Midship section of one-third-scale frigate hull model tested in the sagging condition (mm)

Moatsos, 1. 2005


Appendix 6, Tables

AnnasuriaOverall us Results

Outer Bottom Side Shell Deck Inner Bottom Guedes Soares Paik

Diff "10 Diff "10 Diff% Diff% Diff"lo Diff "10

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Sa!1 Hog Sag Hog

0 3.419 3.419 7.472 7.472 3.120 3.120 No Inner Bottom 1.994 1.502 1.994 1.502

2.5 3.419 3.419 7.472 7.472 3.120 3.120 1.994 1.502 1.994 1.502

5 3.419 3.419 7.472 7.472 3.120 3.120 1.994 1.502 1.994 1.502

7.5 3.323 3.030 7.496 7.557 2.956 2.444 1.933 1.008 1.981 1.490

10 3.226 2.779 7.518 7.596 2.786 1.992 1.884 0.853 1.965 1.478

12.5 3.126 2.622 7.539 7.615 2.612 1.705 1.852 0.813 1.949 1.464

15 3.023 2.523 7.558 7.624 2.430 1.524 1.830 0.817 1.931 1.450

17.5 2.921 2.462 7.576 7.629 2.245 1.413 1.816 0.848 1.912 1.436

20 2.814 2.425 7.591 7.632 2.055 1.344 1.807 0.901 1.891 1.420

22.5 2.705 2.402 7.606 7.634 1.859 1.303 1.802 0.978 1.869 1.404

25 2.596 2.391 7.618 7.635 1.658 1.277 1.799 1.079 1.846 1.387

Table 6.1 Percentile differences in US theoretical models used for Annassuria FPSO.

SchiehallionOverall us Results


Diff% Diff% Diff 0"- Diff% Diff% Diff "10

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Sag Hog Sa!1 Hog

0 6.078 6.078 4.430 4.430 4.510 4.510 No Inner Bottom 1.980 2.168 1.980 2.168

2.5 6.078 6.078 4.430 4.430 4.510 4.510 1.980 2.168 1.980 2.168

5 6.078 6.078 4.430 4.430 4.510 4.510 1.980 2.168 1.980 2.168

7.5 5.967 5.640 4.379 4.229 4.411 4.117 1.915 1.774 1.964 2.149

10 5.856 5.369 4.327 4.117 4.312 3.873 1.875 1.657 1.947 2.130

12.5 5.745 5.203 4.276 4.057 4.212 3.723 1.851 1.629 1.931 2.111

15 5.633 5.101 4.226 4.023 4.111 3.633 1.838 1.631 1.914 2.091

17.5 5.519 5.038 4.178 4.004 4.009 3.578 1.830 1.650 1.897 2.071

20 5.406 5.001 4.131 3.993 3.906 3.544 1.825 1.682 1.880 2.051

22.5 5.291 4.978 4.088 3.987 3.803 3.523 1.822 1.730 1.864 2.031

25 5.176 4.964 4.047 3.984 3.700 3.511 1.820 1.795 1.848 2.011

Table 6.2 Percentile differences in US theoretical models used for Schiehallion FPSO.

TritonOverall us Results


Diff% Diff "10 Diff% Diff% Diff "10 Diff"lo

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Saa Hog Sag Hog

0 1.437 1.437 10.571 10.571 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.041

2.5 1.437 1.437 10.571 10.571 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.041

5 1.437 1.437 10.571 10.571 . 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.041

7.5 1.223 0.844 10.726 11.209 3.543 2.970 -0.560 -0.971 5.884 -0.602 5.822 -0.172

10 1.097 0.520 10.886 11.637 3.353 2.476 -0.708 -1.298 5.929 -0.672 5.845 -0.190

12.5 0.967 0.318 11.051 11.912 3.157 2.162 -0.855 -1.492 5.953 -0.671 5.866 -0.209

15 0.836 0.193 11.221 12.085 2.957 1.969 -0.978 -1.604 5.966 -0.663 5.886 -0.253

17.5 0.701 0.115 11.396 12.193 2.755 1.848 -1.118 -1.674 5.972 -0.657 5.906 .().272

20 0.565 0.068 11.577 12.259 2.545 1.774 -1.255 -1.715 5.976 -0.643 5.924 "().291

22.5 0.427 0.040 11.764 12.300 2.330 1.730 -1.390 -1.740 5.978 -0.613 5.941 ..().310

25 0.285 0.023 11.957 12.324 2.111 1.702 -1.520 -1.755 5.980 ..().559 5.956 .().329

Table 6.3 Percentile differences in US theoretical models used for Triton FPSO.

Paik LRPASS

FPS03

Sagging 12.754*10IlNmmHogging 11.559*1012NmmSagging 17.96*1012NmmHogging 16.28*1012NmmSagging lO.56*lOI2NmmHogging 6.45*1012Nmm

13.13661012Nmm11.9438 lO'2Nmm

19.33 lO'2Nmm14.372 lOl2Nmm9.7546* lOl2Nmm7.1630*1012Nmm

FPSOI

FPS02

Table 6.4 FPSO Ultimate Strength Results.

Moatsos, I. 2005


PropertlM .. ing P8ik a Lee (1897) MuIII

SlMSY lip ElIperiIMnI ALPS/ISUII CeIcuI8tecl EmIr~_1EJp EmIr,_lILPSIIIIIIlI

Model ~ a: ss _I Palk IIUSACT Palk IIUSACT PaIk IIUSACT

DowIIng2 H 1 0.6.s9 -, 0.450 233.500 0.684 0.723 0.722 0.721 5.263 5.132 -0.139 -0.277

0.789Dowhg" H { Q:a56' 0.856 256.800 0.844 0.856 0.858 0.867 1.632 2.653 0.233 1.269

0.984DowlIng 10 H ;'0 .•7-63. 0.610 641.720 0.736 0.755 0.810 0.805 9.136 8.571 6.790 6.211

0.745Nishihata MST3 S 0.672 0.672 83.960 0.715 0.619 0.759 0.733 5.797 2.456 18.445 15.553

NishIhsra lIST" S 0.785 0.785 109.960 0.805 0.747 0.818 0.816 1.589 1.348 8.680 8.456

"'_II H 0.445 0.756 219.900 0.632 0.618 0.621 0.620 -1.771 -1.935 0.483 0.323

DowFdaBM S 0.537 0.537 1502.000 0.644 0.652 0.632 0.647 -1.899 0.464 ·3.165 -0.773

H: Hogging, S:Sagging. CF: Compression Flange, SS: Side Shell

l6XP.etmel')taJ· .Table 6.5 Properties of equivalent cross sections and comparison of ultimate strength formulations with

test models and numerical results.

Moatsos, 1. 2005

CHAPTER7CORROSION EFFECTS ON SHIP STRUCTURES

7.1 Introduction

In the past decade, several casualties of merchant ships have occurred while they were

under operation and one of the possible causes for such casualties is thought to be the

structural failure of aging ships in rough seas and weather. Clearly, in such cases the

structures that started out being adequate somehow become marginal later in life. Corrosion

and fatigue-related potential problems are considered to be the two most important factors

potentially leading to such age-related structural degradation of ships and, of course, many

other types of steel structures. Graff (1981) defines corrosion, for both metals and non-

metals, as:

"The deterioration of a solid body through interaction with its environment. That is,

destruction through unintentional chemical or electro-chemical reaction beginning at itssurface. "

Even though the term corrosion is used to describe the destruction of metals, paint and

rubber deterioration by sunlight or chemicals is also a form of corrosion and the

deterioration of the ceramic lining in a furnace or the hardening and cracking of plastics in

heat or sunlight may also be considered as forms of corrosion. In distinguishing the types of

corrosion that occur on metallic and non-metallic materials, the terms wet and dry corrosion

are sometimes used.

The term wet corrosion is used from the fact that in electrochemical corrosion the

electrolyte involved is moist. Almost all metals suffer corrosion to some extent due to the

action of the water and the atmosphere and they often corrode from electrochemical action

because of their crystallographic nature (electrons are free to move through their lattice

structures). Electrochemical corrosion involves the presence of an electrolyte in contact with

the metal. An electrolyte can be any conducting substance, but it usually is an aqueous

solution of a salt, acid, or alkali.

Moatsos, I. 2005

Chapter 7.Corrosion Effects on Marine Structures 250

The term dry corrosion results from the fact that chemical corrosion In non metallic

materials occurs in the absence of a liquid phase or above the dew point of the environment.

In the case of non-metallic materials, these are usually resistant to the attack of mildly

corrosive media, such as water and the atmosphere but they are also attacked by certain

chemical agents under certain specific conditions. Such type of corrosion is usually caused

by various chemicals in gaseous or vapour form, often in high temperature.

7.2 Corrosion Mechanism

Metals usually exist in nature in combined forms such as oxides, hydroxides, carbonates,

sulphides, sulphates and silicates. For the metal to be refined to its pure form and to be

extracted a considerable amount of energy is spent thus making a refined metal to be of a

much higher energy state when compared to its unrefined ore. If we look at the problem of

corrosion from a metallurgical point of view, the definition of corrosion of a metal is

extractive metallurgy in reverse, according to Fontana and Greene (1967), i.e. the natural

tendency of the material to seek the lower energy level contained in its combined state. We

define as rust the dark-reddish brown coating which forms on iron or steel in a moist or wet

environment and consists of a hydrated form of ferric oxide (Fe203). It is common to

reserve the term "rust" for steel and iron corrosion whereas for other metals when they form

oxides on their surfaces, they are said to simply corrode.

The corrosion of electrochemical corrosion of metals in aqueous electrolytes is associated

with the flow of electric current between anodic and cathodic areas within the system as it

can be seen in (Fig. 7.1) in the Appendix. Two distinct regions exist within the system:

• The Anodic Region, where the metal atoms are transformed into positive ions and

free electrons.

• The Cathodic Region, where the free electrons unite with ions of the electrolyte to

produce either hydrogen or oxygen.

Corrosion occurs in the anodic region, i.e. where the dissolution of the metal causes metal

ions to go into solution. The surface of one component may become the anode and the

surface of another component in contact with it the cathode. Usually, corrosion cells will be

much smaller and more numerous, occurring at different points on the surface of the same

Moatsos, I. 2005


component. Anodes and cathodes may arise from differences in the constituent phases of

the metal itself, from variations in surface deposits or coatings on the metal or from

variations in the electrolyte as it can be seen in (Fig. 7.2). As already mentioned, the metal

may be immersed in an electrolyte, as in (Fig. 7.3) or the electrolyte may be present only as

a thin condensed or adsorbed film on the metal surface. The rate of corrosion is influenced

considerably by the electrical conductivity of the electrolyte. Pure water has poor electrical

conductivity and the corrosion rate will be much lower than sayan acid solution of high

conductivity.

Corrosion of iron (Fe) in an aqueous electrolyte can be described, according to Jastrzebski

(1976) as:

1. In the absence of oxygen, Hydrogen Evolution

(7.1)

Solid Liquid Solid Gas

The corroding metal simply supplies ions to replace the hydrogen ions in the electrolyte.

This type of reaction usually occurs in acid environments. The anodes are usually large

areas while the cathodes small areas. The electrons freed by the dissolution of the corroding

metal flow through the metal to the small cathodic areas where the hydrogen is released.

2. In the presence of oxygen, Oxygen Absorption

(7.2)

In neutral (PH=7) aqueous electrolyte, or one that is slightly alkaline, iron corrodes in the

presence of oxygen. In this case the electrons are freed by the dissolution of the metal are

intercepted by the oxygen according to

(7.3)

Moatsos, I. 2005


The free electrons are converted to hydroxyl ions. In this case the anodic areas on the

surface of the metal are due to cracks in the oxide film coating the metal. Consequently, the

anodic areas are very small, whereas almost the entire surrounding surface of the metal

constitutes the cathode. The corrosion current is concentrated within a very small area and

causes a very strong, localized attack.

With the presence of sodium and chlorine ions in solution in seawater, one of the best

electrolytes existing in nature, the cathodic product of this form of corrosion is sodium

hydroxide and the anodic product is ferrous chloride. Both product are readily soluble and

will diffuse away from their respective electrodes. As they meet in solution, ferrous

hydroxide is precipitated. With the presence of sufficient oxygen, ferrous hydroxide

oxidizes to ferric hydroxide, which precipitates even more quickly. As a result of the

tendency of both products on the electrodes to diffuse away, the corrosion will continue in

the presence of enough oxygen. In cases where agitation of the solution occurs, as with

waves and currents offshore, the rate of corrosion increases as the aeration of the solution

increases.

7.3 General Forms of Corrosion

Depending on the surrounding environment, the process of corrosion can occur in various

forms:

1. Concentration Cell Corrosion

Occurring as a result of differential aeration, where part of the metal body is exposed to

a different air concentration than another part. A difference is created in between the

differently aerated areas and the surface area exposed to the electrolyte of low-oxygen

concentration is anodic whereas the surface area exposed to high-oxygen concentration

is cathodic with the flow of electrons between the two areas termed as a differential

aeration current. This particular form of corrosion occurs just below the waterline for

metals that are partially immersed in seawater. Dissolution of the metal just below the

waterline releases electrons that flow through the metal body to the highly aerated

region, just above the waterline. The electrons are said to flow through the metal circuit,

or the external circuit. In the cathodic area oxygen combines with the free electrons to

form hydroxyl ions. The internal circuit of the corrosion cell consist of the migrant of

Moatsos, I. 2005


the metal ions through the electrolyte. The amount of oxygen available controls the

magnitude of the corrosion current.

A drop of water on a steel or iron surface constitutes a simple example of concentration

cell corrosion, which can be seen in (Fig. 7.4). The central portion of the surface

covered by the drop is farthest from the oxygen of the air and becomes anodic, while the

outer periphery of the surface covered by the drop has ready access to oxygen and

becomes cathodic. The spot of rust forms at the centre of the drop of water. In a moist

environment this form of corrosion occurs where some object rests on a metal surface

and screen that portion of the surface from oxygen access. For example, steel plate will

rust under a block of wood that is left lying for some time. Steel or iron equipment

exposed to the weather for a long time will rust because of the stagnant films of water

left in recesses on the metal surface. Corrosion from differential aeration leads to pitting

on the surface.

2. Galvanic Corrosion

Galvanic Corrosion is electrochemical corrosion that occurs when two dissimilar metals

are n contact with one another in an electrolyte. A potential difference naturally occurs

between the two dissimilar metals when they are immersed in an electrolyte. If the two

metals are physically touching, or if they are otherwise electrically connected, the

potential difference causes an electron flow between them. The less corrosion resistant

metal becomes anodic and corrodes, and the more corrosion resistant metal becomes

cathodic. The cathodic metal corrodes very little or not at all in this situation. The

chemical reaction at the cathode may be either hydrogen evolution or oxygen absorption

depending on the nature of the corrosive environment. The free electrons, resulting from

the anodic metal transforming into ions and going into solution, flow through the

electrical junction between the two metals and are intercepted by positive ions from the

solution at the cathode.

Chemists have developed values of standard electrode potentials for metals completely

free of oxide films on their surfaces. In reality most metals are covered with oxide films

which tend to make their electrical potentials more positive, making their surfaces more

protected from attack in corrosive environments and as a fact galvanic corrosion occurs

between two corroding metals. With most engineering metals being alloys and not pure

Moatsos, I. 2005


metals, only rarely are these alloys in equilibrium with their ions in solution. To account

for environmental conditions met in practical applications the galvanic series exists of

the most often used industrial metals and alloys in ascending order from the most easily

corroded to the ones least likely to corrode. The series can be found in (Table 7.1) in the

Appendix with Noble denoting the materials least likely to corrode (gold and platinum).

The position of a material in the galvanic series agrees with the position of its

constituent element in the series of standard electrode potentials. When two of these

materials, which are adjacent or closely separated in the series, are coupled, there is little

danger of galvanic corrosion as a result of the small relative electric potential generated

between the two materials, whereas more rapid corrosion will occur from two materials

whose listing are farther apart in the galvanic series. While the series provides a better

representation of actual galvanic corrosion characteristics than the series of standard

electrode potentials, the corrosion processes tend to change with time. The product of

corrosion may accumulate at either the anode or the cathode, or both, and lead to a

reduction of the process.

3. Atmospheric Corrosion

The atmospheric form of corrosion primarily occurs as a result of the moisture and

oxygen in the air. A classification exists in the types of atmosphere that exist and a

particular type may be classified as Industrial, Marine and Rural. Industrial and Marine

atmospheres frequently contain such gaseous products as sulphur dioxide, hydrogen

sulphide and sodium chloride. These products tend to increase corrosion rates,

especially in the presence of moisture.

The oxidizing action of the air on the exposed metal surface brings about film

formation, and electrochemical action causes the breakdown of the film, a process

which occurs when there is moisture in the air according to Hanson and Hurst (1969).

With most oxide films absorbing moisture, the presence of an electrolyte is certain and

although the film created may prevent corrosion taking place, should it crack or be

destroyed through mechanical impact or abrasion, new metal will be exposed and

concentration cells will be developed. Rain could also wash away part of the oxide film, in

addition to providing moisture, unless the particular oxide that has formed is exceptionally

adhesive. In addition to this rain also removes accumulated corrosion products that help

Moatsos, I. 2005


slow down the rate of corrosion and lead to an increase of the atmospheric corrosion rate

following rain.

Gaseous sulphur compounds of the atmosphere in the presence of moisture produce acids

which increase the conductivity if the liquid layer on the metal surface. Sodium chloride in

marine atmospheres also increases conductivity of the liquid on the metal surface. In the

case of atmospheric corrosion the corrosion rate is controlled by the supply of moisture to

the metal surface compared to corrosion of metals immersed in a solution where the

corrosion rate is controlled by the volume of oxygen available.

The primary product of iron and steel corrosion is ferrous hydroxide, which oxidizes to

hydrated ferric oxide (red rust) and forms a non adherent film which falls away easily from

the surface. The addition of copper, nickel and chromium in small amounts (tenths of 1%)

improves the resistance of steel to atmospheric corrosion since such alloys cause steel to

form tighter, more protective rust films. Nickel and copper form insoluble sulphates during

atmospheric corrosion that do not easily separate from the metal surface. Stainless steels

have the best corrosion resistance characteristics and the galvanizing of steel is also

common for atmospheric corrosion protection.

7.4 Corrosion in the Marine Environment

Ship structures operate in a complex environment. Water properties such as salinity,

temperature, oxygen content, pH level and chemical composition can vary according to

location and water depth. Also the inside face of plates will be exposed to aggressive

environments existing in cargo tanks. The structures are often protected, either with paints

or with cathodic systems that deliver a current intensity to the protected metal surface

inhibiting the corrosion process.

7.5 Mechanics of Corrosion in TankerlFPSO Structures

In a paper proposing a time-dependent corrosion wastage model for single and double

hulled TankerlFSOIFPSO structures Paik et al. (2003) provides an excellent description of

the mechanics of corrosion in tanker-type structures. According to that description corrosion

appears as non-protective, friable rust, largely on internal surfaces that are unprotected.

Over time, the rust scale continually breaks off, exposing fresh metal to corrosive attack.

Moatsos, I. 2005


Thickness loss cannot sometimes be judged visually until excessive loss has occurred.

Failure to remove mill scale during construction of the vessel can accelerate the corrosion

experienced in service. Severe corrosion, usually characterised by heavy scale

accumulation, can lead to significant steel renewals. In addition to general (uniform)

corrosion, which reduces the plate thickness uniformly, there are other types of more

localised corrosion patterns identifiable in ships, which can be seen in (Fig. 7.5) The most

important of these are:

• Pitting: Pitting is a localised form of corrosion that typically occurs on bottom

plating, other horizontal surfaces, and at structural details that trap water,

particularly at the aft bays of tanks. In coated surfaces pitting produces deep and

relatively small diameter pits that can lead to patches (e.g. 800 mm diameter),

resembling a condition of general corrosion. Severe pitting can lead to significant

steel renewals.

• Grooving: Grooving corrosion is localized, linear corrosion that occurs at structural

intersections where water collects or flows. This corrosion is sometimes referred to

as "in-line pitting attack" and can also occur on vertical members and flush sides of

bulkheads in areas of flexing.

• Weld Metal Corrosion: Weld metal corrosion is defined as preferential corrosion of

the weld deposit. The most likely reason for this type is galvanic action with the

base metal, which may initially lead to pitting. This often occurs in hand welds as

opposed to machine welds.

In fact pitting can lead to leakage but in general, because it is much localised, it does not

affect the in-plane stress distribution in a plate. In any case, pitting is accounted in this study

along with the other types of corrosion and general corrosion since the corrosion wastage

measurements used have been collected for all types of corrosion and are mathematically

modelled as a monotonic decrease in plate thickness.

In most existing TankerlFPSO vessels, one can distinguish five types of cargo and ballast

tanks spaces:

• Segregated Ballast Spaces

Moatsos, I. 2005


• Cargo/Clean Ballast Spaces

• CargolDirty Ballast Spaces

• Cargo/Storm Ballast Spaces

• Cargo-Only Spaces

The areas of the ship most exposed to corrosion are wing ballast tanks, due to exposure of

seawater, humidity, a salty atmosphere when empty, and increases in temperature when

deck and sides are exposed to sunlight. Combined ballast and cargo tanks are somewhat less

exposed to corrosion. They are however exposed to water washing, which can destroy the

protective oil film, thus exposing fresh steel for corrosion. In cargo-only tanks, the bottom

area may suffer from acidic water setting out from the oil. At the sides and the top of these

tanks, the oil normally provides a form of protection. The time in ballast is typically 50% of

the first two types of spaces and much less, around 5%, for the third. Cargo-only tanks are

exposed to cargo about 50% of the time and are typically empty for the rest of the time.

The frequency of filling heavy ballast holds is decided by characteristics of the trade route

and weather conditions. In loading and unloading cargoes at harbour, empty cargo holds

may be partly filled with ballast water to adjust trim, which increases the possibility of wet

and dry cycles, affecting corrosion rates therein. The type of cargo carried also affects

corrosion rates. Typically in tankers, certain types of oil can lead to higher corrosion. For

example, sour crude is worse than a sweet one, and cargoes that are higher in oxygen

content, such as gasoline, lead to higher corrosion rates.

In any type of vessel, corrosion rates in a compartment depend on the structural component

location and orientation and the type of corrosion protection employed. In ballast tanks,

which are normally coated, corrosion will start in with coating breakdown and in high stress

zones, such as ends of structural elements and free edges of cut-outs. Significant corrosion

of elements in ballast tanks adjacent heated cargo tanks or tanks with consumables is also

possible. An increased degree of local structural flexibility has been claimed to increase

corrosion rates as time progresses. This is apparently because of serial increases in scale

loss and structural flexibility. Locations of necking and grooving are disproportionately

affected.

Moatsos, I. 2005


It is important to realize that the corrosion process of ship structures can be different from

that of "at-sea" stationary immersion corrosion. Temperature inside ballast or cargo tanks

can be warmer that that of at sea. In loading and unloading cargoes at harbour, ballasting

and debaIIasting will also occur in order to adjust freeboard or trim. Such ballast cycles may

accelerate the corrosion process because the steel surface becomes repeatedly dry or wet by

seawater.

Where coatings are present the process of corrosion will normally very much depend on the

degradation characteristics of such anticorrosion coatings. Structural flexing resulting from

wave loading could also increase corrosion rates due to the continuing loss of scale and

exposure of new surface to corrosion. Although most classification societies usually

recommend carrying out of maintenance for the corrosion protection system in time, this

may not universally be the case in reality unless safety is likely to be compromised.

The life (or durability) of a coating can in a specific case correspond to the time when a

predefined and measurable extent of corrosion starts after either:

1. The time when a ship enters service

2. The application of coating in a previously bare case

3. Repair of a failed coating area in an existing structure to a good intact standard.

The life of coating typically depends on the type of coating systems used, details of its

application (e.g. surface preparation, stripe coats, film thickness, humidity and salt control

during application, etc.), and relevant maintenance and other factors. The coating life to a

predefined state of breakdown is often assumed to follow the log-normal distribution

according to Yamamoto and Ikegami (1998). After the effectiveness of the coating is lost,

some transition time, that is, duration between the time of coating effectiveness loss and the

time of corrosion initiation, may be considered to exist before the corrosion "initiates" over

a large enough and measurable area. The transition time is often considered to be an

exponentially distributed random variable according to Yamamoto & Ikegami (1998).

Apart from the coating of steel with various types of corrosion protective paints, the most

commonly applied form of corrosion protection in the marine environment is that of

utilising cathodic protection. Such process of electrochemical metal corrosion prevention or

Moatsos, I. 2005


reduction makes the protected metal the cathode of the corrosion process. Electronic current

supplied to the metal comes from sacrificial galvanic anodes or impressed current through

insoluble electrodes or expandable auxiliary anodes. Cathodic protection offers one of the

most effective means of corrosion control and is extensively used by the offshore and

shipping industries

In the case of Sacrificial Galvanic Anodes these are bars of metal welded or bolted to the

metal structure to be protected and are made of magnesium, zinc, aluminium or alloys of

these metals which have a negative potential below that of the metal to be protected.

Current flows continuously from the sacrificial metal through the welded or bolted joint into

the metal to be protected making it the cathode of the corrosion cell. Good quality sacrificial

anodes develop insignificant anodic polarization during their service lives and have a low

rate of dissolution according to Sansonetti (1969). The electrical current produced by one

sacrificial anode amounts to only a few hundred milliamperes and hence a number of

anodes are required for protection of structures depending on their size. (Fig. 7.6) shows

some of the various sizes and shapes of sacrificial anodes as different sizes and shapes are

available for every requirement in length-ta-weight and surface area-ta-weight ratios.

For Impressed Current Cathodic Protection the system can be best explained through the

use of an example as described in Graff (1981). If the steel structure to be protected and an

expandable auxiliary electrode are immersed in an electrolyte and the two are wired or

connected electrically through a battery or de rectifier so that the negative side of the battery

is connected to the steel structure, and the positive side is connected to the auxiliary

electrode, electrons will flow from the auxiliary electrode through the battery to the steel

structure, making it cathodic or negative. Positive ions released into the electrolyte at the

auxiliary electrode travel through the electrolyte to the protected structure and complete the

electric circuit. Electron protective flow, before application of an external source of

electrical power is limited to the difference in local electrode potentials divided by the sum

of the electrical resistances in both the cathodic body and the auxiliary anode. To prevent

corrosion, external electrical power is supplied through the battery or de rectifier to boost

the flow of electrons to the protected structure, although the phrase "flow of electrons" is a

paradox considering that by convention, positive electricity flows from positive to negative.

Auxiliary electrodes for the impressed current system in the form of expendable anodes are

made from the same materials as sacrificial anodes for galvanic corrosion protection. The

Moatsos, I. 2005


some of the most common materials used for inert impressed current electrodes in offshore

applications include graphite and high-silicon iron, steel and lead-silver-antimony alloy but

also the more expensive platinized titanium and platinum clad titanium due to their long

lifetime of 5-7 and 20 years in seawater respectively.

Guedes Soares (1998) studied the effect of general corrosion in decreasing the thickness of

the plating and considered that repair actions were performed whenever the plate thickness

would decrease below a defined limit value. It was shown that in the steady-state situation

with frequent inspections the expected value of plate thickness depends on the repair criteria

and is independent of the corrosion rate. The steady-state situation only occurs whenever

there are several plate replacements during the ship's life and thus at a random point in time,

the plates in the area considered have a thickness that is governed by the replacement

criteria rather than by the corrosion rate. Although this situation may occur in some special

areas of some ship types, the most common situation is for plating to be replaced only once

during the ship's life if at all. Therefore, they will never reach the so-called steady-state

situation and a model is required to describe the transient situation of wastage increase until

plate replacement. In many situations the expected value of reliability at a random point in

time is not enough and informant about the time variation of the reliability is desired.

Guedes Soares and Garbatov (1996) proposed a model to describe the time-dependent

reliability of a ship hull in which the plates are subjected to corrosion and repair actions.

However the effect of corrosion was represented by an uncertain but constant corrosion rate,

which resulted in a linear decrease of plate thickness with time.

7.6 CorrosionModels

Until now, the fleet of FPSOs has been relatively small in number when compared to the

number of bulk carriers or tankers operating today worldwide. The structural flexibility

characteristics of ocean-going single- or doubles-skin tankers may be different from those

of FPSOs, which load and unload a lot more frequently, sometimes every week. Such

frequent loading/unloading patterns for FPSOs may accelerate the corrosion process. On the

other hand, FPSOs typically operate at a standstill at a specific sea site, and this aspect may

likely mitigate the dynamic flexing, keeping the corrosive scale static, compared with that

of ocean-going vessels. The two counter aspects may then offset the positive and negative

effects of corrosion. While further study is pending, it is considered that the corrosion

Moatsos, I.2005


models often defined for ocean-going single-or double-skin tanker structures can be applied

to corrosion prediction of structures of FPSOs as long as the corrosion environment is

similar.

The conventional models of corrosion assume a constant corrosion rate, leading to a linear

relationship between the material lost and time. Experimental evidence of corrosion

reported by various authors show that a non-linear model is more appropriate. Southwell et

al. (1979) observed that the wastage thickness increases non-linearly in a period of 2-5

years of exposure, but afterwards it becomes relatively constant. This means that after a

period of initial non-linear corrosion, the oxidised material that is produced remains on the

surface of the plate and does not allow the continued contact of the plate surface with the

corrosive environment, stopping corrosion. Southwell et al. (1979), proposed a linear, (Eq.

7.4), and bilinear, (Eq. 7.5), model which were considered appropriate for design purposes

in mm and where 1 is measured in years.

d = 0.076 + 0.038t

d = 0.090t, 0.00 s t s 1.46d = 0.076 + 0.038t, 1.46 s t s 16.00

(7.4)

(7.5)

Both models are conservative in the early stages in that they overestimate the corrosion

depth, which might occur at the initial phases of the corrosion process.

Melchers & Ahammed (1998) suggested a steady-state model for corrosion wastage

thickness, which is given by:

d = 0.170t 0 s t s 1d = 0.152+0.01861 1s t s 8d = -0.364 + 0.0831 8 ~ t ~ 16

(7.6)

and they also proposed a power approximation for the corrosion depth given as:

d = 0.1207t06257 (7.7)

Moatsos, I.2005


Yamamoto (1998) has presented results of the analysis of corrosion wastage in different

location of many ships, exhibiting the non-linear dependence of time and a tendency of

levelling off. All reference to these early works shows that the non-linear time dependence

of corrosion rates has been already identified experimentally.

7.6.1 Linear Corrosion Model [Paik, Lee, Hwang and Park (2003)]

Paik et al. (2003) have proposed a time dependent corrosion wastage model .specifically

based on measurements from Single- Double-Hull and FSOs and FPSOs. (Fig. 7.7) is a

graphical representation of the proposed model for a coated area in a marine steel structure.

The corrosion behaviour in this model is categorised into three phases, on account of:

1. The durability of the coating

2. The transition to visibly obvious corrosion

3. The progress of such corrosion

The curve showing corrosion progression, as indicated by the sold line in (Fig. 7.7), is

convex, but it may in some cases be concave (dotted line). The convex curve indicates that

the corrosion rate (i.e. the curve gradient) is increasing in the beginning but is decreasing as

the corrosion progress proceeds. This is due to the fact that corroded material stays on the

steel surface, protecting it from contact with the corrosive environment and the corrosion

process stops. This type of corrosion progression may be typical for statically loaded

structures so that relatively static corrosion scale at the steel surface can disturb the

corrosion progression. On the other hand the concave curve (dotted line) in (Fig. 7.7)

represents a case where the corrosion rate is accelerating as the corrosion progression

proceeds. This type of corrosion progression may be likely to occur in dynamically loaded

structures, such as ship structures, where structural flexing due to wave loading continually

exposes additional fresh surface to the corrosive attack.

The corrosion behaviour can be expressed as a function of the time (year) as:

(7.8)

(7.9)

Moatsos, I. 2005


where t, is the depth of corrosion wastage in mm, rr the annualized corrosion rate in mm per

year, T,the time of exposure under the corrosion environment in years, which may be taken

as:

(7.10)

with T the age of the vessel in years, T; the life of the coating in years, T, the duration of

transition in years and Cl. C2 the corrosion coefficients. T,can be taken as 0 indicating that

corrosion starts immediately after the breakdown of coating. Although the coating life Te, to

a predefined state of breakdown must be a random variable, it is treated as a constant

parameter in this case.

The coefficient C2 in (Eq. 7.8) and (Eq, 7.9) determines the trend of corrosion progress,

while the coefficient Cl, is in part indicative of the annualized corrosion rate, r.; which can

be by differentiating (Eq. 7.8) with respect to time. These two coefficients closely interact,

and in principle they can be simultaneously determined based on carefully collected

statistical corrosion data for existing ship structures. However, this approach is in most

cases not straightforward to apply, mainly because of the differences in data collection sites

typically visited over the life of the vessel, and possibly also differing time between visits.

That is, it is normally difficult to track corrosion at a particular site based on the typically

available thickness gauging data for ships, which are mostly obtained at periodic inspections

(surveys) of different "representative" regions of the structure. This is part of the reason for

the relatively large scatter of corrosion data in many studies.

An easier alternative is thus to determine the coefficient Cl at a constant value of the

coefficient C2. This is mathematically a simpler model, but it does not negate any of the

limitations arising due to usual methods of data collection in surveys. It does, however,

make possible the postulation of different modes of corrosion behaviour over time

depending on the value adopted for C2 alone in an easy-to-understand way.

For corrosion of marine structures, some past studies indicate, according to Paik et al.

(2003), that the coefficient C2 may be typically in the range of 0.3-1.5. Clearly the

coefficient C2 affects the implied trend of the corrosion progress. For the purpose of

Moatsos, I. 2005


practical design C2=1 can be used, with the corrosion behaviour perhaps linearised over

convenient and small enough extents of time. Then (Eq. 7.8) and (Eq. 7.9) can be simplified

to:

(7.11)

(7.12)

The only coefficient to be left undetermined is Cl for now while re is treated as a constant

parameter.

The sources of uncertainty involved in corrosion data are various, as already mentioned in

previous sections, and the coating life is also a factor in such uncertainties. In corrosion loss

measurements, information on the coating life is normally unclear. In fact, a 5-year coating

life is considered to represent an undesirable situation, whereas 10 years or longer is a

relatively more desirable state of affairs.

7.6.2 Non-Linear Corrosion Model [Guedes-Soares & Garbatov (1999)]

The corrosion wastage mathematical model, of which a graphical representation can be seen

in (Fig. 7.8), proposed by Guedes Soares and Garbatov (1999) and adopted in this study,

uses a non-linear function of timethat describes the growth of corrosion on three different

phases:

1. In the first phase, it is assumed that there is no corrosion because the corrosion

protection system is effective. Failure of the protection system will occur at a

random point of time and the corrosion wastage will start a non-linear growing

process with time. The first stage depends on many factors and statistics, according

to Emi et al. (1994), show that in ships it varies in the range of 1.5-5.5 years. In (Fig.

7.8) t belongs to [0' ,0].

2. The second phase is initiated when the corrosion protections is damaged and

corresponds really to the existence of corrosion, which decreases the thickness of the

plate. In (Fig. 7.8) t belongs to [O,B]. This process was observed to last a period

around 4-5 years in typical ship plating according to Maximadj et al. (1982).

Moatsos, I.2005


3. The third phase corresponds to a stop in the corrosion process and the corrosion rate

becomes zero. In (Fig. 7.8) t>B. Corroded material stays on the plate surface,

protecting it from the contact with the corrosive environment and the corrosion

process stops. Cleaning the surface or any involuntary action that removes that

surface material originates the new start of the non-linear corrosion growth process.

The formulation uses the asymptotic value of corrosion wastage as input for creating an

exponential function of time that describes the effect of corrosion and thus can be applied

for the reliability assessment of different plate elements. The model can be described by the

solution of a differential equation of the corrosion wastage:

dood(t)+ d(t) = d; (7.13)

where d; is the long-term thickness of the corrosion wastage, d(t) is the thickness of the

corrosion wastage at time t and d (t ) is the corrosion rate.

The solution of (Eq. 7.13) can have the general form:

(7.14)

and the particular solution leads to:

(((-Te)]

d(t)=doo l-e T, ,

(7.15)

where tC is the coating life, which is equal to the time interval between the painting of the

surface and the time when its effectiveness is lost and t; is the transition time, which may be

calculated as:

Moatsos, I. 200S


doc"(=--I tga

(7.16)

where ais the angle defined by OA and OB in (Fig. 7.8)

The model adopted in addition to being a more flexible alternative to all other suggested,

once the long-term corrosion wastage and the duration of the corrosion process is known,

also generalises the concept by including an early phase with the corrosion protected surface

and free parameters that can be adjusted to the data in specific situations.

7.6.3 Combining Corrosion l\1odel [Qin and Cui (2001)]

In the Melchers (1999) model, the corrosion protection system (CPS) was not considered

while in Guedes Soares & Garbatov (1999) model and Paik et al. (2003) model the CPS was

considered. However, in these models, the corrosion was assumed to start immediately after

CPS effectiveness is completely lost or more accurately they define the instant as CPS life

when the general corrosion starts. No interaction between the CPS and the environment was

considered. In reality, the CPS such as coating will deteriorate gradually and the pitting

corrosion may start before the CPS loses its complete effectiveness as described in

Yamamoto and Ikegami (1998). According to Qin and Cui (2001), if one defines a

parameter q as the degree of effectiveness of the CPS, when the CPS is new and fully in

function, (q=I); when the CPS completely loses its effectiveness (q=O). This time should be

defined as the life of the CPS. Therefore for each CPS, two parameters Tst and Tel may be

used to describe its corrosion protection function. 1'..vt is the instant at which the pitting

corrosion starts which can be measured. Tel is the life of the CPS at which the general

corrosion starts. If we assume that the degree of effectiveness of the CPS is a measurable

quantity, then Tel can also be measured if we apply the CPS to a non-corrosive material such

as Titanium.

Due to the fact that many factors such as location, environmental conditions and stress

levels will affect the life of the CPS, both Tst and Tel may be best modelled as random

variables. By distinguishing the corrosion initiation life as Tst and the life of the CPS as Tel,

one can reach the conclusion that in the state of pitting corrosion progress both the CPS and

the environmental parameters (macro and micro) will affect the corrosion rate. The

Moatsos, I. 2005


corrosion rate can then be defined by equating the volume of pitting corrosion to uniform

corrosion. Regarding this as the transition period, the corrosion rate increases and the

particular period can also be termed as the acceleration period. With the complete loss of

effectiveness of the CPS, general corrosion starts and the corrosion rate decreases as a result

of the increasing thickness of the corrosion product and the microbial biomass. As a result

of all of the above and according to Qin and Cui (2001) we can subdivide the corrosion

process, in a similar way as already described in Guedes Soares' approach in the previous

section, into three stages as it can be seen in Fig (7.9):

1. A no corrosion stage during which the CPS is fully effective and t belongs to [O,Ts,]

2. A stage where corrosion accelerates when the pitting corrosion generates and

progresses and t belongs to [Tsh TA]

3. A stage where corrosion decelerates and t belongs to [TA, Td where TL is the life of

the structure or the time at which repair and maintenance action takes place.

In practice the corrosion accelerating life TA may be different from the CPS life Tel and at Tel

a change in the corrosion rate may occur. However we assume in this case that TA=Tel.

A Wei bull function is used to describe the corrosion rate and hence in this corrosion model

the corrosion rate is modelled as:

r{t)= 0

r(t}=d_~(t-:. r_1-('-;'nO~t~Tst

(7.17)

where doo,P,T],Tst are four model parameters to be determined. The maximum corrosion

rate occurs when:

1

TA =T: =T. +1/(P;lyTA = Tst

P>l (7.18)

P~1

and the value is:

Moatsos, I. 2005


P=1 (7.19)

rmax =~ 00 P<1

The instants at which the corrosion rate reaches the maximum under different conditions

can be seen in (Fig. 7.9). Using this corrosion model, the wear thickness due to corrosion

can be calculated from:

d{t}= 0

d(ll=d_{-exp[ _(,-;" rJ} (7.20)

The proposed model is flexible and can be fitted to most of the situations, once the four

parameters d"",P,7],Tst are known.

7.7 Other Types of Corrosion

A number of other types of corrosion exist and, although they are not examined in detail in

this thesis, can contribute to general wastage corrosion once coating breakdown occurs or

the CPS ceases to operate efficiently and therefore should be described in some detail. Such

types are Biological Corrosion, Stress Corrosion and Corrosion Fatigue.

a) Biological Corrosion, although not strictly a type of corrosion occurs from the

deterioration of metal by various corrosion processes as a result of metabolic activity

of living micro-organisms. These micro-organisms are found in fluidized mediums

with pH values from 6 to 11 (seawater pH is 8), in temperatures from -1.1 °c to 82°C

and under pressures up to 98 MPa.

The normal metabolic activities of micro-organisms affect corrosion in seawater by:

i. Altering anodic and cathodic reactions

11. Changing surface films

Moatsos, l. 2005


iii. Creating corrosion conditions (differential aeration)

The two classes of micro-organisms that exist are: aerobic, which require oxygen for their

metabolic processes; and anaerobic, which live and grow in environments containing little

or no oxygen according to Cleary (1969). In our case, from these two categories, three types

of micro-organisms are of most concern in sea water corrosion:

I. Sulphate-Reducing Anaerobic bacteria produce the most problems and have

an accelerating influence on the corrosion behaviour of buried pipelines,

piles below the mud-line and deeply submerged steel components. In a low

oxygen environment the bacteria can utilize the hydrogen cathodically

formed at the steel surface to reduce sulphate from the electrolyte and

increase the local corrosivity of the environment. The corrosion result is the

formation of pits on the steel surface filled with black iron sulphide and

ferrous hydroxide products.

II. Thiosulfate-Oxidizing Aerobic bacteria thrive in near neutral pH fluids

containing dissolved oxygen and increase the corrosive conditions by

increasing the local sulphuric acid concentration.

Ill. Iron Aerobic bacteria assimilate ferrous iron from the electrolyte and

precipitate ferrous hydroxide as tubercles or nodules on the steel surface.

This accumulation tends to produce crevice corrosion.

IV. Furthermore fouling organisms, such as barnacles, may enhance localised

corrosion during which differential aeration cells are created and sometimes

the excrement of the organism itself may cause increased corrosion.

As a preventative measure to biological corrosion a number of different organic coatings are

used in marine applications, as it can be seen in (Fig. 7.10), depending on the area to be

coated.

b) Stress Corrosion is defined as the cracking of a metal under the combined effect of

tensile stresses and a corrosive environment. Stress cracking is a very distinct type

and differs from ordinary cracking caused by hydrogen embrittlement as the second

type occurs when atomic hydrogen evolving at the metal surface in a hydrogen

sulphide rich solution diffuses into the metal collecting in vacancies and dislocations

Moatsos, I. 2005


and lowering metal strength and ductility. As it can be seen from (Fig. 7.10) stress

corrosion cracking progresses in a direction perpendicular to the existing tensile

stress, whose type can be either applied, residual from forming or welding or

thermal. Almost no physical evidence of the formation of stress corrosion cracking

is visible since the cracks are very fine until the latter stages of corrosion. The

corrosion pit or gouge which forms on the metal surface acts as a stress raiser and

corrosion and the tip of the notch causes the stress corrosion crack to start there.

This type of corrosion is highly localised and failure that might occur from this type

resembles brittle fracture. The most common way of preventing stress corrosion is

cathodic protection

c) Corrosion Fatigue is defined as the reduction of the metal fatigue resistance caused

by the presence of a corrosive medium. Cracks resulting from fatigue propagate

faster in the presence of cyclic stresses that expand the lattice of the metallic

structure with the frequency of stress cycle application having a pronounced effect

on corrosion fatigue, especially at low frequencies where the metal lattice in

expanded or strained condition has a significantly longer contact time with the

corrosive environment. Again as in stress corrosion, corrosion fatigue is most likely

to occur in solutions or electrolytes that cause pitting attack with the corrosion pit

serving as a stress raiser and crack initiator. Ferrous alloys submerged in seawater

tend to lose the fatigue limit characteristic of their behaviour for stress-cycling in air.

The term fatigue limit indicates the particular cyclic stress level applied to the metal

below which the metal will cycle an infinite number of times without fracture. In

seawater steels appear to show continually decreasing ability to withstand cyclic

stresses as the number of cycles of stress application increases. (Fig. 7.12) in the

Appendix demonstrates the relationship of metal corrosion fatigue behaviour when

compared with in-air fatigue behaviour.

7.8 Discussion-Conclusions

7.8.1 Results

After an investigation of the corrosion occurrmg on manne structures a number of

interesting remarks can be made as far as this area of the analysis is concerned. Corrosion of

the hull results in a reduction in modulus and hence an increase in applied stress for a given

bending moment. In conjunction with this, a reduction in local strength occurs and the two

Moatsos, 1.2005


effects combine to give a lower factor of safety against collapse. The amount and

distribution of corrosion which takes place depend on a number of factors which include the

quality and maintenance of surface coatings, environmental conditions such as temperature

and humidity, the frequency of tank washing, the type of cargo carried and mechanical

action such as stress reversal which can remove protective scales and hence speed the

corrosion process. Two forms of wastage are typically found in ships:

1. General overall reduction in thickness.

2. Localised pitting of the surface.

The latter, which is unlikely to affect the buckling resistance significantly, is typically found

in bottom plating and on horizontal surfaces where corrosive substances can accumulate.

The former is more usual in decks and in the uppermost shell and bulkhead structures where

maintenance is more difficult to carry out and where conditions of high humidity exist.

Using the theories described in the previous sections of this chapter, a study was carried out

investigating the effects of various corrosion models on US formulation for stiffened plates

and the overall hull girder US that would help to determine the best strength model for use

in reliability analysis and to help shape the proposed models and approach. As briefly

mentioned in Chapter 6, the aforementioned approaches and corresponding formulation was

incorporated into computer code in Visual Basic running in MS Excel 2003 called

MUSACT (Moatsos Ultimate Strength Analysis with Corrosion and Thermal effects) to

analyse and to compare the results obtained by the formulation and with all of the 3 FPSO

vessels analysed. A sample window of the code is MS Excel 2003 can be seen in (Fig. 7.13)

with the Corrosion Model Data window and the Results & Reports window visible. The

corrosion models for the 2 approaches in the MUSACT code can be seen in (Fig. 7.14) and

(Fig. 7.15) for deck and bottom plating respectively. In all cases no repairs are assumed.

It is assumed that for the first 5 years of the vessel's life there is no break-down in the CPS

after which corrosion follows each of the models for a total of 30 years assuming that no

repairs are carried out on the structure. This can be very close to reality as FPSO structures

hardly ever leave their assigned locations and are rarely repaired or serviced while on

service. Stopping production to dry-dock the vessel would incur huge loss of profit to the

owner and operator and such practices have very rarely occurred. Looking at the two

Moatsos, I.2005


corrosion modelling approaches it is interesting to note that both produce very similar

results after 30 years of corrosion, a fact that occurs from the maximum wastage used in

each of the approaches being similar, but throughout the life of the vessel the amount of

corrosion wastage that each of the approaches calculates, varies with the linear model

underestimating the values by as much as 2 times compared with the non-linear approach.

Hence it was decided to proceed to reliability analysis by using the non-linear approach and

avoid the conservative linear method that would oversimplify the mathematical modelling

of the phenomenon and add more assumptions and simplifications to this analysis.

As the Guedes Soares-Garbatov approach was selected as more suitable for use in our

reliability analysis, the code also investigated the influence of the transition time on the on-

linear model and the results of the analysis can be seen in (Fig. 7.16) for deck plating with 5

years duration of coating, but also the influence of long-term corrosion depth on the non-

linear model used, the results of which can be seen in (Fig. 7.17) for 5 years transition time

and 5 years coating duration.

As it can be seen from (Fig. 7.18) for sagging hull girder US and (Fig. 7.19) for hogging

hull girder US clearly when combined with the different US formulation, the results can

vary with the US results following the "trends" and shape curves of the corrosion models

used demonstrating that the corrosion model to be chosen will influence greatly both the.

strength and reliability results to be obtained. As it can be seen from (Table 7.2) for

Anassuria the difference is in the range of 3.4% for the OB, 7.5% for SS, 3.1% for the

Deck, 2% for Sagging US and 1.5% for Hogging US for no corrosion between the Paik

simplified formulation plate US approach and the author developed analytical approach

with the Paik approach providing more conservative results. In a similar fashion the results

for Schiehallion can be seen in (Table 7.3) and for Triton in (Table 7.4).

7.8.2 Proposal on alternative corrosion formulation

It was not possible to apply to the analysis all the corrosion models that were described in

(Chapter 7) as a results of the time constraints set for this study. The two basic corrosion

models as proposed by Paik et al. (2003) and Guedes Soares & Garbatov (1999) were

implemented in the MUSACT code and compared demonstrating the differences that can

arise when using a linear and non-linear corrosion model respectively. This leaves room for

further comparison and improvement of the MUSACT code through the utilisation of the

Moatsos, I. 2005


Qin & Cui (2001) approach that combines both mathematical models and can utilise

essentially both approaches by modelling effectively different phases of the corrosion

process and using the same format. The approach was described in detail in previous

sections of this chapter along with a detailed comparison of the three models can be found

in Qin & Cui (2001). When b=l , (Eq. 7.20) can be rewritten as:

(7.21)

• which is essentially the corrosion model proposed by Guedes Soares & Garbatov (1999).

When 17=1. if one applies the Taylor series expansion in (Eq. 7.20) and only keeps the

linear term one can obtain:

(7.22)

• which is essentially the corrosion model as proposed by Paik et al. (2003). Then when:

doc = 0.1207 TSI = 0 17= 1 f3 = 0.6257 (7.23)

• then essentially the model becomes:

d{t) = 0.1207to.6257 (7.24)

• which is essentially the corrosion model proposed by Melchers (1999). This demonstrates

the flexibility of the approach and would definitely improve the MUSACT code if it is

incorporated in the analysis in the future.

Moatsos, I. 2005


Chapter 7, Reference:

Cleary, H.J. 1969, "On the Mechanism of Corrosion of Steel Immersed in Saline Water",OTe Preprints, Vol. 1, Paper No. 1038.

Emi, H., Arima, T., Umino, M.A. 1994, "A Study on Developing a Rational CorrosionProtection System of Hull Structures", NKK Technical Bulletin, pp 65-79.

Fontana, M.B., Greene, N.D. 1967, Corrosion Engineering, The McGraw -Hill BookCompany.

Georgia State University Department of Physics and Astronomy HyperPhysics Website[Online. Internet], Available: http://hyperphysics.phy-astr.gsu.edu/hbaselhframe.html,Accessed: 26/01/05.

Gordon England Consultants Website [Online. Internet.]

Available: www.gordonengland.co.uk, Accessed: 26/01/05.

Graft, W.J 1981, Introduction to Offshore Structures, Design-Fabrication-Installation,Chapter 12Corrosion, The Gulf Publishing Company, Houston Texas USA, pp 239-258.

Guedes Soares, C., Garbatov, Y. 1996, "Reliability of Maintained Ship Hulls Subjected toCorrosion", Journal of Ship Research, Vol. 40, No.3, pp 235-243.

Guedes Soares, C., Garbatov, Y. 1998, "Reliability of Plate Elements Subjected toCompressive Loads and Accounting for Corrosion and Repair", Structural Safety andReliability, Vol. 3, Rotterdam: Balkema, pp 2013-20120.

Guedes Soares, C., Garbatov, Y. 1999, "Reliability of Maintained, Corrosion ProtectedPlates Subjected to Non-Linear Corrosion and Compressive Loads", Marine Structures,Elsevier Publishing, Vol. 12, pp 425-455.

Hanson, H.R., Hurst, D.C. 1969, "Corrosion Control: Offshore Platforms" OTC Reprints,Vol. 1, Paper No. 1042.

Jastrzebski, Z.D. 1976, The Nature and Properties of Engineering Materials, 2nd Edition,Chapter 15, John Wiley and Sons Publishing.

Maximadj, A.I., Belenkij, L.M., Briker, A.S., Neugodov, A.U. 1982, "TechnicalAssessment of Ship Hull Girder", Petersburg: Sudostroenie (in Russian).

Melchers, R.E. 1998, "Probabilistic Modelling of Immersion Marine Corrosion", StructuralSafety and Reliability, Balkema, pp 1143-1149.

Melchers, R.E. 1999, "Corrosion Uncertainty modelling for Steel Structures", Journal ofConstructional Steel Research, Vol. 52, pp3-19.

Paik, J.K., Lee, J.M., Hwang, J.S., Park, Y.l2003, "A Time-Dependent Corrosion WastageModel for the Structures of Single- and Double-Hull Tankers and FSOs and FPSOs",Marine Technology, Vol. 40, No.3, pp 201-217.

Paik, J.K., Thayamballi, A.K., Kim, S.K., Yang. S.H. 1998, "Ship Hull Ultimate StrengthReliability Considering Corrosion", Journal of Ship Research, Vol. 42(2), pp 154-165.

Peterson, M.L. 1975, "Corrosion Fatigue of Offshore Welded Steel Structures", OceanEngineering, November 1975.

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http://hyperphysics.phy-astr.gsu.edu/hbaselhframe.html,

http://www.gordonengland.co.uk,


Qin, S., Cui, W. 2001, "A New Corrosion Model for the Deterioration of Steel Structures inMarine Environments", Proceedings of the I" International ASRANet Colloquium,Glasgow Scotland, UK.

Sansonetti, S.J. (1969) "To Prevent Corrosion at Sea: Think Aluminium Anodes", OTCPreprints, Vol. 1, Paper No. 1040.


Southwell, CR., Bultman, J.D., Hummer Jr, C.W. 1979, "Estimating of Service Life ofSteel in Seawater", Seawater Corrosion Handbook, Noyes Data Corporation, New JerseyUSA, pp 374-387.

Sun, H.H., Bai, Y., 2000, "Reliability Assessment of a FPSO Hull Girder SUbjected toDegradations of Corrosion and Fatigue", Proceedings of the International Society ofOffshore and Polar Engineers (lSOPE), Vol. VI, pp 355-363.

Wirsching, P.H., Ferensic, J., Thayamballi, A.K. 1997, "Reliability with respect to UltimateStrength of a Corroded Ship Hull",Marine Structures, Vol. 10(7), pp 501-518.

Yamamoto, N. Ikegami, K. 1998, "A Study on the Degradation of Coating and Corrosion ofShip's Hull Based on the Probabilistic Approach", Journal of Offshore Mechanics andArctic Engineering, No. 120, pp 121-128.

Yamamoto, N. 1998, "Reliability Based Criteria for Measures to Corrosion", Proceedingsof the I1h International Conference on Offshore Mechanics and Arctic Engineering(OMAE'98), Safety and Reliability Symposium, New York, USA, ASME.

Moatsos, 1. 2005


Appendix 7, Figures

Electron flow \,....._." ",~I '_-"" I

Electrolyte

~--~~r--- ~~ __- +veions-+

+- -ve ions

Cathode

Figure 7.1 Flow between anodic and cathodic areas (Gordon England, 2005).

Figure 7.2 Anodic and cathodic areas resulting from surface variations (Gordon England, 2005).

Atmosphere

Figure 7.3 Corrosion process in an aqueous electrolyte (Gordon England, 2005).

Moatsos, I. 2005


T~ hydroYicEIQUP::kl~'oxld,:esto brm f\Jst

waterdroPletIron hydrQAlde

lormc andpre~ipial~s

FIp.t1rnchp.mirJ'l10311action drivenby the energy ofoddanon continu5!$the eorroslonprocess,

;"''..-2, . OH 0

Fe' 2I '. /

:;athOde acton·tlUJOt;;~ I,;xy~1I'rom Q r, f,:>rr'l'ling,ydro1ddQ ions.

Figure 7.4 Corrosion of iron (Fe) in an aqueous electrolyte (Georgia State University, 2005).

(a) (b) (c)

Figure 7.5 Types of corrosion wastage: a)general, (b) localized, (c) fatigue cracks from localisedcorrosion (Paik, Lee, Hwang & Park, 2003).

BOLT-ON TYPES

WELD-ON AND CLAMP-ON

~~~

6 II • II 1)

• I. J 11

~161nCLAMPS

OR

HANGING TYPES

~2.1' 2.7 ...

~~141'O

~

~B.ACKETS

Figure 7.6 Various anode shapes (Craft, 1981).

Moatsos, 1. 2005


Transition

Durability • .1 .i . Progress of corrosionof coating I

IIIIIII

Tc Tc+1jStructure age T (years)

Figure 7.7 Paik, Lee, Hwang and Park proposed corrosion model (Paik, Lee, Hwang & Park, 2003).

0'

o

T. T,

L- A! '1i i! /IIl !;

d,

o B

Figure 7.S Guedes Soares and Garbatov proposed corrosion model (Guedes Soares & Garbatov, 1991).

0.5

~=O.s

- 0.4...a:JCD~

0.3E.s--- 0.2...

0.'

0.0

o Tst 5 10 15 20 25

t (years)

Figure 7.9Qin & Cui suggested corrosion model (Qin &Cui, 2001).

Moatsos, I. 2005


Figure 7.10 Selector for organic coatings (Fontana & Green, 1967).

Direction of crackpropagation

1

Figure 7.11 Stress corrosion cracking (Jastrzebski, 1976).

_..TENSILESTRENGTH OFMATERIAL

AIR FATIGUE

AIR FATIGUE LIMITCORROSION FATIGUE

LOG, (LIFE OR CYCLES TO FAILURE)

Figure 7.12 S-N Diagram for corrosion fatigue (Craft,1981).

Moatsos, I. 2005


r,t:. 1: • ~ n I !II

... '~.. ,

: u

1 to '~].. .-

00

r:~="""=4;::.;;:••".'---111 !Cwb~," ('"') I

L~-"'''''''''!L"_·'''''__ '''...JII .'/20031

I

,-- _s_ ..·........_ _ ...,_ ..._-- :::' -- ..... :::' ..... :::' OiH~- - - - '" ..._IUU.•~ "ut.' ·" .. ;Ul ..~ U .•~ .0... ·,Ull ..~. ,... ,-

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._ -., .,,," tKIU ,.•.-.... - ·"1)11 tlu•.' ....:-tlH'

_.-.... u

G••

.- MU' .• -wn4 MlM.1 .....~H. ..-~-.. n.'

._ -.• ~~.Ut?._, -.. ._.~N' .. -W))t -,_, ....".~... n.1 -.tItI.U - U.• .~"-.• .,."", ....•.\ UtI

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U.. .~ .... un ,_ .... ,_ ,.... ,_ - un 'M,U

._ ,_"" un Uf1 1.1'1:1 ,.... •m ...

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..."", n..._ 14._ :M.,MI.M,UN '~.'14 U.*H 1".UtM.UQ In.n U.ltH H.T"'"

~ .. uu ,. ..... 1"'1'1.1 l'U1fll

" • • ~L~L DebuQ ~ Results,(Jnt /

l.tMH HU1t !LN." u..u'.MAI ItUM "'.~" U.*41T.MNI ItU" ".et"' n,.utUIUt ....,., M."" !4.ln'l.'lU. IN.)UlJ....." n.-l.' __ OU lJ.)" D.,",

u.~ !It.''' o."l1 U ....1._ 'M.Ul U_ U.....,.

,.,... 'lI.1Il1._. n.JM1

~D[...... I~·" "DO:JRoody

Figure 7.13 MUSACT VB Code for MS Excel2003 displaying corrosion and results windows.

Corrosion Models Deck Plating

2.5

2.0EE 1.5.......Q)

f 1.0c0.~ 0.5...8

0.00 10 20 30 40

Time (Years)

- Guedes-Soares &Garbatov (1999)

- Paik, Lee, l-lwang, Park(2003)

Figure 7.14 Influence of corrosion models on deck plating wastage.

Moatsos, I. 2005


1.400

1.200

1.000ES 0.800Cl)Cl

! 0.600e0 0.400.~......8 0.200

0.000

Corrosion Models Bottom Plating

•__...-- /

.: ~

I ;1'/

/ ,"/

~

f •,/I /"

l,r'

_ Guedes-Soares &Garbatov (1999)

- Paik, Lee, Hwang, Park(2003)

o 10 20Time (Years)

30 40

Figure 7.15 Influence of corrosion models on bottom plating wastage.

Influence of Transition Time on The Non-Unear Guedes Soares & Garbatov (1999)Model (Deck Plating-5 Years Duration of Coating)

Transition Time(Years)

Corrosion Time (Years)

Corrosion Wastage(mm)

• 2.000-2.500

o 1.500-2.000

o 1.000-1.500

• 0.500-1.000

00.000-0.500

Figure 7.16 Influence of transition time on the non-linear Guedes Soares & Garbatov (1999) model.

Moatsos, I. 2005


Influence of long-term corrosion depth on the Non Linear Guedes Soares &Garbatov (1999) Model (5 years transition time, 5 Years coating duration) ~----~

I D 1.8O(}2.000• 1.600-1.80001.400-1.600• 1.200-1.400o 1.000-1.200• 0.80(} 1.000o 0.600-0.800o 0.400-0.600.0.200-0.400o 0.000-0.200

Long Term Corrosion(Years)

2.000

1.800

1.600

oCorrosion Time (Years)

Corrosion Wastage(mm)

Figure 7.17 Influence of long term corrosion depth in the Guedes Soares & Garbatov (1999) non-linearmodel.

Effect of Corrosion & Plate Strength Models in Sagging US

-14000

-14500

-15000Ez~ -15500(J):::J

-16000

-16500

-170000

~ Paik Q)r.lPaik St.Rate

___ Paik Q)r.lFaulkner St.Rate

.. Soares-Garbatov Q)r.lPai

St.Rate~ Soares-Garbatov

Cor JFaulkner st. Rate

5 10 15 20 25 30Time (Years)


Moatsos, I. 2005


16000

15500

15000

14500

14000

Effect of Corrosion & Plate Strength Models in Hogging US

I~.

____ Paik Cor.lFaulkner St.Rate

Soares-Garbatov Cor.lPaikSt.Rate

~ Soares-GarbatovCor./Faulkner SI.Rate

o 5 10 15 20 25 30Time (Years)


Moatsos, I. 2005


Appendix 7, Tables

Anodic, least noble, most readily corroded

Magnesium and magnesium alloysZincCommercially pure aluminumCadmiumAluminum alloy (4.5% Cu, 1.5% Mg, 0.6% Mn)Steel or ironCast ironChromium stainless steel, 13% Cr (active)High nickel cast iron18% Cr, 8% Ni steel (active)18% Cr, 8% Ni, 3% Mo steel (active)Hastelloy C (active) (62% Ni, 18% Cr, 15% Mo)lead-tin soldersleadTinNickel (active)Inconel (active) (BOOIo Ni, 13% Cr, 7% Fe)Hastelloy A (60% Ni, 20% Mo, 20% Fe)Hastelloy B (65% Ni, 30% Mo, 5% Fe)Chorimet 2 (66% Ni, 32% Mo, 1% Fe)Brasses (Cu-Sn)CopperBronzes (Cu-Sn)Copper-nickel alloysMonel (70% Ni, 30% Cu)Silver solderNickel (passive)Inconel (passive) (80% Ni, 13% Cr, 7% Fe)Chromium stainless steel, 13% Cr (passive)18% Cr, 8% Ni steel (passive)18% Cr, 8% Ni, 3% Mo steel (passive)Hastelloy C (passive) (62% Ni, 18% Cr, 15% Mo)Chlorimet 3 (62% Ni, 18% Cr, 18% Mo)SilverTitaniumGraphiteGold and Platinum

Cathodic, most noble, least likely to corrode-------

Table 7.1 The Galvanic Series (Craft, 1981).

AnnasuriaOverall us Results


Diff% Diff% Diff% Diff% Diff% Diff%

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Sag Hog Sag Hog

0 3.419 3.419 7.472 7.472 3.120 3.120 No Inner Bottom 1.994 1.502 1.994 1.502

2.5 3.419 3.419 7.472 7.472 3.120 3.120 1.994 1.502 1.994 1.502

5 3.419 3.419 7.472 7.472 3.120 3.120 1.994 1.502 1.994 1.502

7.5 3.323 3.030 7.496 7.557 2.956 2.444 1.933 1.008 1.981 1.490

10 3.226 2.779 7.518 7.596 2.786 1.992 1.884 0.853 1.965 1.478

12.5 3.126 2.622 7.539 7.615 2.612 1.705 1.852 0.813 1.949 1.464

15 3.023 2.523 7.558 7.624 2.430 1.524 1.830 0.817 1.931 1.450

17.5 2.921 2.462 7.576 7.629 2.245 1.413 1.816 0.848 1.912 1.436

20 2.814 2.425 7.591 7.632 2.055 1.344 1.807 0.901 1.891 1.420

22.5 2.705 2.402 7.606 7.634 1.859 1.303 1.802 0.978 1.869 1.404

25 2.596 2.391 7.618 7.635 1.658 1.277 1.799 1.079 1.846 1.387

Table 7.2 Percentile differences in US theoretical models used for Annassuria FPSO.

Moatsos, I.2005


SchiehallionOverall us Results

Outer Bottom Side Shell Deck Inner Bottom Guedes Soares PaikDiff% Diff% Djff% Djff% Djff% Djff 0..-

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Sag Hog Sag Hog

0 6.078 6.078 4.430 4.430 4.510 4.510 No Inner Bottom 1.980 2.168 1.980 2.1682.5 6.078 6.078 4.430 4.430 4.510 4.510 1.980 2.168 1.980 2.1685 6.078 6.078 4.430 4.430 4.510 4.510 1.980 2.168 1.980 2.168

7.5 5.967 5.640 4.379 4.229 4.411 4.117 1.915 1.774 1.964 2.14910 5.856 5.369 4.327 4.117 4.312 3.873 1.875 1.657 1.947 2.130

12.5 5.745 5.203 4.276 4.057 4.212 3.723 1.851 1.629 1.931 2.11115 5.633 5.101 4.226 4.023 4.111 3.633 1.838 1.631 1.914 2.091

17.5 5.519 5.038 4.178 4.004 4.009 3.578 1.830 1.650 1.897 2.07120 5.406 5.001 4.131 3.993 3.906 3.544 1.825 1.682 1.880 2.051

22.5 5.291 4.978 4.088 3.987 3.803 3.523 1.822 1.730 1.864 2.03125 5.176 4.964 4.047 3.984 3.700 3.511 1.820 1.795 1.848 2.011

Table 7.3 Percentile differences in US theoretical models used for Schiehallion FPSO.

Triton

Outer Bottom Side Shell Deck Inner Bottom Guedes Soares PaikDiff% Diff% Diff% Diff% Diff% Diff%

Years Paik Guedes Paik Guedes Paik Guedes Paik Guedes Sag Ho!! Sa!! Hog

0 1.437 1.437 10.571 10.571 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.0412.5 1.437 1.437 10.571 10.571 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.0415 1.437 1.437 10.571 10.571 3.732 3.732 -0.412 -0.412 5.801 -0.041 5.801 -0.041

7.5 1.223 0.844 10.726 11.209 3.543 2.970 -0.560 -0.971 5.884 -0.602 5.822 -0.17210 1.097 0.520 10.886 11.637 3.353 2.476 -0.708 -1.298 5.929 -0.672 5.845 -0.190

12.5 0.967 0.318 11.051 11.912 3.157 2.162 -0.855 -1.492 5.953 -0.671 5.866 -0.20915 0.836 0.193 11.221 12.085 2.957 1.969 -0.978 -1.604 5.966 -0.663 5.886 -0.253

17.5 0.701 0.115 11.396 12.193 2.755 1.848 -1.118 -1.674 5.972 -0.657 5.906 -0.27220 0.565 0.068 11.577 12.259 2.545 1.774 -1.255 -1.715 5.976 -0.643 5.924 -0.291

22.5 0.427 0.040 11.764 12.300 2.330 1.730 -1.390 -1.740 5.978 -0.613 5.941 -0.31025 0.285 0.023 11.957 12.324 2.111 1.702 -1.520 -1.755 5.980 -0.559 5.956 -0.329

Overall US Results

Table 7.4 Percentile differences in US theoretical models used for Triton FPSO.

Moatsos, I. 2005

CHAPTERS

LOADS, STOCHASTIC PROCESSES AND THEIR

COMBINATION

8.1 Introduction

The accurate prediction of loads and load effects is a fundamental task in the design of ship

structures which in general consists of three major aspects:

• The prediction of still water resultant loads and load effects

• The prediction of wave resultant loads and load effects

• The prediction of combined loads and load effects

The occurrence of still water loads exists from forces that result from the action of the ship

self-weight. the cargo or deadweight and the buoyancy. They include bending moment.

shear force and lateral pressure and remain constant under specific loading conditions.

However. still water loads may vary from one load condition to another as a result of a

variation of the aforementioned parameters and need to be considered as stochastic

processes in the long term. Typically. the most important still water load component is the

still water bending moment (SWBM).

Wave loads are forces resulting from wave action and include vertical, horizontal bending

and Torsional moments. shear forces. hydrodynamic pressure and transient loads such as

springing and slamming. Due to the random nature of the ocean, wave loads are stochastic

processes both in the short-term and in the long term. The most typical and important

component of wave loading is the vertical wave bending moment (VWBM).

Since still water loads and wave loads are of quite different random natures. their respective

extreme value has been thought that would not occur at the same time in most cases. For the

appropriate determination of rational values of the extreme combined loads. a load

combination theory needs to be employed that considers each random load as a stochastic

process in the time domain and combines two or more loads as scalar or vector processes.

Moatsos, I.2005

Chapter 8.Loads, Stochastic Processes and their Combination 287

Mansour and Thayamballi (1993) have addressed the issue of different load combination

problems for ships and the primary types are:

• Hull girder loads, i.e., vertical bending, horizontal bending and Torsional loads

• Hull girder loads and local pressure loads

• Hull girder loads and transient loads, i.e., springing, slamming or whipping

moments.

The major hull girder loads of design interest are the vertical and horizontal bending

moments and shear forces and sometimes the Torsional moments depending on the ship

type such as in the case of multi-hulls or containerships which have low Torsional rigidity

and therefore Torsional loads are of primary importance. In most, merchant vessels that do

not have wide hatches, such as tankers with closed sections, Torsional stresses are

nevertheless small. Horizontal bending moment and shear force excited by low frequency

waves are of less concern, due to the fact that they do not result in significant stresses in

ocean-going ship structures. For production marine structures designed for being always

headed on to waves in operation, although the actual heading may be subjected to

uncertainty when wind, current and waves are not collinear, the horizontal bending and

shear effects are negligible. In cases when shear forces need to be accounted for, the focus

may be on the stem quarter body which is likely to have more critical shear forces than the

forward one.

When examining hull girder loads the following are the typical extreme loads and load

combinations of interest.

• Extreme vertical bending loads, with coexisting values of vertical and horizontal

bending and Torsional loads. Vertical bending moments are important in the

midship region.

• Extreme Torsional loads, with coexisting values of vertical and horizontal bending

loads. This needs to be addressed in the forward quarter body of ship structures with

low Torsional rigidity.

Moatsos, I. 2005


Traditionally, the total bending moment M, is defined as the extreme algebraic sum of still

water moment Msw and wave-induced moment Mw, as follows:

(8.1)

where Msw is taken as the maximum value of the still water bending moment resulting from

the worst load condition on the ship in both hogging and sagging. A detailed distribution of

the still water moment along the ship's length can be calculated by a double integration of

the difference between the weight force and the buoyancy force, using simple beam theory.

For merchant ships, the mean value of Msw may be taken as the maximum allowable still

water bending moment provided by a Classification Society. Mw is taken as the mean value

of the extreme wave-induced bending moment which the ship is likely to encounter during

its lifetime. For the safety and reliability assessment of damaged ship structures, short-term

analysis using linear strip theory may be used to determine Mw when the ship encounters a

storm of specific duration, and with a certain small encounter probability. On the other

hand, a long term analysis will be employed to determine Mw for newly built ships. In

calculating Mw, a second-order strip theory may be used to distinguish between sagging and

hogging wave-induced bending moments. To approximately take into account the

correlation between still water and wave induced bending moments, the following equation

can be used for calculating the total bending moment:

(8.2)

where ksw and kw are load combination factors for still water and wave-induced bending

moments, respectively. We can reduce (Eq. 8.2) to (Eq. 8.1) when ksw=kw=1.0. In the post-

accident condition, which is not examined during this study but nevertheless should be

mentioned, the ship should not operate at high speed and should also avoid rough seas,

resulting in it experiencing a reduced (moderate) wave height. Therefore, the related wave-

induced moment may normally be smaller than that for the normal extreme design

condition. When both Msw and Mw are calculated for the intact design case and taken as the

maximum allowable values of still water and wave induced moments provided by a

Classification Society, the ABS SafeHull guide (ABS, 1995) suggest the load combination

coefficients depending on the damage condition as indicated in (Table 8.1). However it

Moatsos, I. 2005


should be noted that when Msw and Mw are calculated by the direct method with specific

loading conditions, operational conditions and sea states the load combination should be

made by (Eq. 8.2) with more relevant factors. To consider dynamic load effects, the total

bending moment can be evaluated from:

(8.3)

, where kd is the load combination factor related to the dynamic bending moment Md arising

from either slamming or springing. Md is taken as the mean value of the extreme dynamic

bending moment in the same wave condition as the wave-induced bending moment, while

the effect of ship hull flexibility is accounted for in the computation of Md. For springing in

very high sea states, Md is normally ignored. For slamming it is approximated by

Md=O.1l5Mw, for tankers in sagging and Md=O in hogging (Mansour, Wirsching et al.,

1994) & (Mansour et al., 1994). Nevertheless there is an immediate effect in sagging but

dynamic response will give a possible large hogging as well.

8.2 Met-Ocean conditions North Sea

While strong winds can occur throughout the North Sea, wave heights vary greatly due to

fetch limitations and depth effects. In areas of shorter fetch, for example the Southern North

Sea, storm waves are shorter, steeper and less high than in the open areas of the Northern

North Sea. The latter is more likely to see greater occurrences of swell, with periods up to

20 sec and which may be the result of remote meteorological systems rather than local

winds. The effects of fetch and depth are shown in (Fig. 8.1) illustrating typical extreme

(lOD-year) wave heights.

Although this thesis does not take into account the effects of wind loads and currents,

explicitly on the structures analysed, it is worthwhile to briefly discuss the subjects.

Currents in the North Sea are considered as a stochastic element, driven by tides, and a

residual component generally dominated by storm driven currents. Currents are an

important consideration in the North Sea as current forces directly impact offshore

infrastructure, and a good description of the current regime is required to ensure the safety

of personnel and the environment. Although the current regime is relatively simple in open

Moatsos, I. 2005


waters, the presence of shallow banks, channels and headlands can lead to a more complex

flow. In these areas the tidal streams are generally high.

The wind regime in the North Sea varies seasonally and is characterised by the passage of

anti-cyclonic systems that often give rise to strong storms. Although these storms can occur

n the summer, it used to be though that they tend to be considerably weaker as the low

pressure associated with them is less intense. Nevertheless global warming has changed this

and often violent storms can occur even during the summer. The most intense winds and

waves occur within the frontal systems associated with the anti-cyclonic depressions.

Generally, the strongest winds occur between the southwest and northwest sectors.

However, in the Central North Sea, as it can be seen from (Fig. 8.2), strong winds and

waves can occur in the east sector due to passage of frontal systems westward from the

Skaggerak. Wind loads have to be considered when helicopter operations and smoke

dispersion is taken into account in an analysis and often wind tunnel testing is the best

method to visualise the effect of the wind on the structure, as it can be seen from (Fig. 8.3)

In terms of the long-term variability, decadal and greater, the intensity of storms has been

related to climatic indices such as the North Atlantic Oscillation (NAO). For example, it has

been reported that the 1990s experienced stronger storm conditions, likely to be a result of

the positive NAO during the early part of the decade. When the NAO Index is positive, the

westerly flow across the North Atlantic and Western Europe is enhanced, leading to higher

winds and waves.

8.3 Assumptionsmade

Hydrostatic pressure acting on the side shell will induce transverse stresses in the bottom

plating as well as local bending stresses in the side shell. As the hull strength programs that

were used to validate the MUS ACT code developed for the determination of the US of the

hull girder were restricted to the application of bending loads alone, these additional

components were not taken into account.

As also stated on Chapter 6 of this thesis, transverse stress in the bottom structure resulting

from pressure on the side shell have been estimated to be approximately 4% of the yield

stress for tanker type structures according to Rutherford & Caldwell (1990). This level of

Moatsos, I.2005


stress will have a negligible influence on the axial-carrying capacity of the structure and has

therefore been ignored. Overall bending of the bottom structure between bulkheads and

girders has been similarly ignored on the basis that the resulting longitudinal plating tension

in the vicinity of these members will be counteracted by compression in the remaining

structure. Lateral pressure effects on a local level considered in the analysis are therefore

restricted to:




strain data. Slamming effects are treated separately and combined with the overall loading

as described in (Section 8.7) of this Chapter.

8.4 Modelling Still Water Bending Moment (SWBM)

It has been widely accepted and described in Moan and Wang. (1996) that the SWBM can

be efficiently modelled as a Poisson rectangular pulse process in the time domain as

illustrated in (Fig. 8.4). The reason behind such a conclusion lies in the fact that the SWBM

at a given section of the ship is constant under a specific load condition but can easily vary

from one load condition to another. The duration of each load condition can also be a

random variable.

The space variation of still waters mostly depends on the amount of cargo a vessel is

carrying and the cargo's distribution along the length of the ship. A number of measures are

often taken to ensure that the maximum specified still water loads are not exceeded during

ship operation. Captains are often encouraged by Classification Societies, Local

Government Maritime Regulations and the IMO to load their ships in a way not

dramatically different from those reference conditions given in the ship's loading manual, in

the hope that maximum values are not exceeded. Reality far differs from such suggestions

as advances in technology have allowed for the application of computerized load

distribution procedures, giving captains the freedom to load their vessel in any way they

seem fit as long as the maximum loads are within the specified allowable limits. As a result

of that the loading manual is less likely to be followed and a large variation of load

Moatsos, I. 2005


conditions results from human decisions involved and unfortunately such freedom of choice

could also lead to a larger probability of load exceedance due to human errors in the choice

of load conditions for which very limited control exists worldwide with decisions laying

solely in the hands of the captain and the operator. Moan & Jiao (1988) describe such

examples observed during the operation of an offshore production ship.

The available statistical results have shown that a normal distribution may be considered as

appropriate for the SWBM in conventional ships: cargo ships, containerships and tankers.

FPSOs could be considered as 'modified tankers' as their construction often results from

tanker conversions and even in newly built vessels their hull shape is rather similar to that

of tankers. One could then easily suggest that the SWBM statistics for tankers would be

applicable for FPSOs. As a result of the special characteristics of FPSOs, in particular due

to their frequently changing load distribution, which results from loading and offloading the

vessel, the SWBM in FPSOs differs from the one in tankers and other conventional ships.

Loading conditions specified in the loading manual of FPSOs include docking, normal

operating and severe storm conditions, but the maximum SWBM is controlled by an on-

board computer rather than the load manual, before a new load condition during operation is

to be approved, according an article published in the Naval Architect (2004). Hence, the

captain (also called the Foreman of the FPSO) is able to determine which tanks are to be

loaded and unloaded or what the cargo distribution along the ship is to be depending upon

his personal judgement or operational convenience. As a result of that, the actual SWBM is,

in fact, randomly determined and should thus be described with a probabilistic model.

Following such an arbitrary operational procedure it may also be reasonable to assume that

individual load conditions are mutually independent.

Based on 453 actual still water load condition recorded during the first two operational

years of an FPSO, with typical duration of each load condition varying from several hours

to one day, Moan & Jiao (1988) found that the cumulative distribution function of the

individual sagging SWBM as shown in (Fig. 8.5) is well fitted by a Rayleigh distribution:

(8.4)

Moatsos, I. 2005


in which M, is the SWBM of an individual load condition, and the scale parameter B is so

determined that the specified maximum SWBM, Ms.o , corresponds to a return period of the

design life To,

(8.5)

in which Vs is the mean arrival rate (i.e. the frequency) of one load condition e.g. vs=1.0 day"

1. Substituting 8 solved from Eq. (8.2) into Eq. (8.1) we obtain

(8.6)

While the sagging SWBM follows a Raleigh distribution, the data reported in Moan and

Jiao (1988) indicate that the hogging SWBM follows an exponential distribution:

(8.7)

According to DNV (2005), the specified maximum SWBM for conventional ships in a

design lifetime of 20 years, Ms.o is given by

M 5.0 = -O.06SCw L2 B(CB + 0.7 Xsagging )

= CwL2 B(0.122S - O.OISC B )(hogging)(8.8) (8.9)

In which L, B and CB are the length, breadth and block coefficient of the ship, respectively,

and Cw is the wave coefficient given by

Moatsos, I. 2005

Chapter 8.Loads. Stochastic Processes and their Combination 294

Cw =10.75_[300-L]% for 1oo<L$;300100

= 10.75 for 300 < L $; 350 (8.10), (8.11), (8.12) 1

III

3

=1O.75_[L-350]2 for L~350150

It should be noted that the rule moments given by (Eq. 8.8) and (Eq. 8.9) are not intended

for FPSOs specifically. The maximum SWBM for FPSOs should be determined on a case to

case basis. As a result of lack of vessel design data that would enable a full analysis of each

case to be considered, an alternative solution based on published research had to be found

that would enable rule moments.

According to the data reported by Moan and Jiao (1988), the maximum midship sagging

and hogging moments specified in the load manual are 72.6% and 79.2% of the

corresponding Rule moment respectively. Within the two first years of operation, however,

the experienced maximum sagging and hogging moments are 75% and 83% of the

corresponding Rule moment, respectively. Although these values are all below the Rule

moments, the experienced maximum moments in two years have already exceeded the

specified maximum moments in the load manual. This situation is allowable since the FPSO

of concern was designed to comply with DNV (2005), although smaller moments may be

achieved if the load manual is strictly followed. Nevertheless, the Rule moments are used as

a convenient reference in this study.

It is also noted that the 20-year maximum sagging and hogging moments are 87% and 112%

of the corresponding Rule moment, respectively, by extrapolating the experienced

maximum moments observed in two years, without accounting for load control. Since load

control is required, however, any moments larger than the Rule moments have to be

rejected. This implies that a truncation of the distribution functions given by (Eq. 8.6) and

(Eq. 8.7) at Ms.o may be considered. Being conservative, no truncation is considered in

further analysis.

In the extreme model assumed for this study, the SWBM was originally assumed to follow a

normal distribution in both hogging and sagging. This slightly conservative approximation

Moatsos.L 2005

U =F-t(l __ l)sw swnsw

(8.13)


was applied in order to simplify the extreme model. When the values J1sw and ~w of the

normal distribution are known, the extreme values may be approximated as a Gumbel law.

The Gumbel parameters can be estimated from:

«: =(l-Fsw)t;

(8.14)

where nsw is the number of occurrences of a particular load condition in the reference

period, r.;' is the inverse cumulative probability density distribution, Fsw is the cumulative

probability distribution and!sw is the probability density function. The mean and standard

deviation of the Gumbel distribution could then be calculated as:

u; =«;+ .L:asw

(8.15)

(8.16)

Fse and!se are then gi ven from:

(8.17)

Fse (x) = exp[- exp{- asw(M se - Usw)}] (8.18)

8.5 Modelling Vertical Wave Bending Moment (VWBM)

As a result of the random nature of the ocean, the VWBM is a stochastic process. It may be

described by either short-term or long-term statistics or probabilistic estimates. The short-

term VWBM corresponds to a steady (random) sea state which is considered as stationary

with duration of several hours. Within one sea state, the VWBM follows a Gaussian

Moatsos, I. 2005


process. The maxima of the VWBM thus follow a Rice distribution. For a narrow-banded

Gaussian process, the Rice distribution reduces to the simple Rayleigh distribution.

The long-term statistics are based on weighted short-term statistics over the reference period

of concern. Typically, design wave loads in classification society rules are specifically

based on long-term statistics, according to Meyerhoff (1991). The long-term prediction of

wave loads is usually based on linear analysis, which is then corrected to account for non-

linear effect, based on experiments and/or full-scale measurements.

The long-term formulation of the response amplitudes of bending moment may be

expressed in many ways, but it is basically a joint probability of x and mo expressed as

(8.19)

where p(xlmo), the probability of x for a given mn; is the conditional density function of x

with respect to ma, which is assumed to be Raleigh distributed. Thus,

. 2

p(x1mo)=(:,} :.. (8.20)

and p(mo) is the probability density of the response variance in the considered sea states. It

depends on several variables such as the wave climate represented by H, and Tz, the ship

heading (J, speed v and loading condition c,

(8.21)

The cumulative long-term distribution is defined by,

Q(x > x;) = J Jp(x Imo )fR (r}drXi 0

(8.22)

And since the cumulative Raleigh distribution is

Moatsos, I.2005


00 X2

Jp(x Imo) = e 2"'0 (8.23)Xi

The probability of exceeding amplitude x for a given mo is given by

00 x2

Q(x> Xi) = Je- 2Il10 IR(r )dro

(8.24)

IR(r) may be a complicated function, or group of functions, that defines the probabilities of

different combinations of the variables H; Tz, B, v and c.

The most important of these variables to consider is the ship heading relative to the

dominant wave direction. Ship speed, which has relatively small effect on wave bending

moment, can be eliminated as a variable by assuming either the design speed or the highest

practicable speed for the particular sea condition and the ship heading under consideration.

The effect of amounts and distribution of cargo and weights, which in turn affects draft and

trim, transverse stability, longitudinal radius of gyration, etc, can be a complicated problem.

Usually, however, it can be simplified by assuming two or more representative conditions

offloading, such as normal full load, partial load and ballast condition. Then completely

independent short and long term calculations can be carried out for all load conditions.

With the above simplifications, we are left with the following variables, to be considered in

the probability calculation: H; T, and 8. The variables are considered to be mutually

independent. The probabilities of different combinations of H, and T, are given in a wave

scatter diagram. The probabilities of each ship heading Bhave to be established for different

cases but in general one can say that they are random.

It is generally accepted that the long-term VWBM may be modelled as a Poisson process.

The peak of each individual VWBM, Mw, can be well approximated by a two parameter

Weibull distribution, as shown in (Fig. 8.6), according to Frieze et al. (1991). Denoting Mw.o

as the maximum VWBM in the reference design period To, the cumulative distribution

function of each individual Mw is then expressed as

Moatsos, I.2005


(8.25)

in which b; is the shape parameter and Vw is the mean arrival rate of one wave cycle. It

would be important to note that the above formulation does not account for the dependence

between individual peaks, while in reality there are correlated within a single sea-state.

Alternatively Mw in (Eq. 8.25) may be considered to refer to the individual maximum

moment of each sea state, in which Vw then becomes the mean arrival rate of one sea-state,

so that mutual dependence of individual moments can be neglected.

8.6 Methods of Load Combination

Although the SWBM and VWBM are related to some common parameters, such as the

mass distribution, a correlation between these two loads seems to be negligible for the

estimation of the extreme bending moment. This is because the extreme VWBM is

dominated by the random environment while the extreme SWBM is associated with the

operational procedure, as described in previous sections of this chapter. In subsequent

analysis, no correlation between the SWBM and VWBM is considered. There may be

correlations in trading ships as ballast may be changed before a storm. FPSOs may be prone

to seeing storms in an unloaded condition as shuttle tankers may arrive early to ensure

production will continue during a storm and will no result in a loss of profit for the oil

company.

To combine the SWBM and VWBM, the following two types of methods may be applied

• Stochastic methods which combine the stochastic processes directly

• Deterministic methods which combine the characteristic values of the stochastic

processes.

Commonly applied stochastic methods include general formulation, the point crossing

method, the load coincidence method and the Ferry Borges method. Commonly applied

deterministic methods include the peak coincidence method, Turkstra's rule and the square

root of the sum of squares (SRSS) rule.

Moatsos, I. 200S


8.6.1 General formulation

All the reasons behind using a stochastic approach for the determination of loads and

subsequently the reliability of the structures will be made more evident in (Chapter 9),

which explains in detail reliability theory and discretized approaches for calculating the

probability of failure of time dependent phenomena and processes. To create a link between

loads and their combination and the use of loads in reliability and to appreciate the

effectiveness of stochastic approaches, it is necessary to describe some of the basic elements

of stochastic process theory before describing and comparing in detail the approaches and

methods available.

As described in detail by Melchers (200 1), if we look at a time dependent random process

by splitting it into smaller and smaller time intervals, we have, in the limit, what might be

called the "instantaneous" approach for dealing with time dependent problems as the time

intervals become so small that they effectively do not differ from time-invariant problems.

If we carefully look at (Fig. 8.7) we can define a stochastic process X(t) as a random

function of time t such that for any point in time, the value of X is a random variable. The

outcome x(t) of X(t) is governed by the probability density function fx(x,t). Of course, the

variable t maly be replaced by any kind of finite or countable infinite set of values, such as

the number of load applications. However, time is convenient.

For each value of t, the observed outcome of X(t) may be plotted; the complete set of such

values over a given time interval is called a "realization" or "sample function", as it can be

seen in (Fig. 8.7). Since X is a random variable, the precise form of the realization cannot be

predicted. However, statements can be made about its statistical properties and the mean of

all possible realizations at any point in time is given from:

(8.26)

where fJx,t) is the probability density function at time t. The correlation between the

realizations at two points in time tt and tz is termed the "autocorrelation function" since it

relates to one realization, as it can be seen in (Fig. 8.7):

Moatsos, I. 2005


(8.27)

where f xx ( ) = d 2Fxx I dX1dX2 is the joint probability density function.

function as :

(8.28)

It can be easily shown that if tz=ti=t. the (auto)covariance function becomes the variance

function a/et):

a; (t) = Cxx (t,t) = Rxx (t,t)- p;(t) (8.29)

The correlation function (matrix) may be defined as:

(8.30)

When the random nature of a stochastic process does not change with time, it is said to be a

"(strictly) stationary" process. This means that all its moments are also independent of time.

When only the mean pit) and the autocorrelation RXX(t],t2), are independent of absolute

time, the process is said to be "weakly stationary" or "covariance stationary". Since the

normal distribution is uniquely described by its first two moments, a weakly stationary

normal process is also strictly stationary. As a direct consequence of a process being

stationary, for Cxx( ) and Rxx( ) only the relative difference, e.g. (t]-t2), is of importance and

(Eq. 8.27) becomes:

Rxx(r)= E[X(t)X(t+r)] (8.31)

Moatsos, I. 2005


and in particular, if T=O,Rxx(O)=E(X2), which represents the "mean square" value of X(t).

The mean (Eq. 8.26) and the correlation (Eq. 8.27) have been defined for a stationary

process as averages over realizations. If they can be defined equally well by the time

average over a single realization of a stationary process, the process is "weakly ergodic". If

the equality holds for all moments of a strictly stationary process, the process is "strictly

ergodic". Ergodicity in the mean can be defined as:

(8.32)

and ergodicity in correlation as:

(8.33)

This property clearly can hold only for stationary processes. It is of considerable practical

value in estimating statistical parameters from one or a few sufficiently long records of the

process. The accuracy obtained will depend on the duration T of available records. Often

stationarity and ergodicity are assumed to hold in the analysis of stochastic process records

unless (and until) there is evidence of the contrary.

If Ydt) and Y2(t) are mutually independent continuous load processes, the probability

distribution in a time interval [O,t] for the sum Y=Y/+ Y2 can be obtained using the

assumption that the upcrossings follow a Poisson distribution

(8.34)

in which v(y,t) is the upcrossing rate of the threshold level Y=y at time t. if Yiit) and Ylt)

are stationary, the upcrossing rate v(y,t)=v(y) is time dependent.

Moatsos, I. 2005


In principle the expected upcrossing rate may be determined by using Rice's Formula

(1954)

00

v(y) = J(z - y)f yy (y, z}liy

(8.35)

The joint probability density function fyy() can be calculated by means of the convolution

integral

(8.36)

By changing the integration variables and order, the resulting upcrossing rate is of the

following triple integral, according to Melchers (2001) and Wen (1990):

V(y) = J J J(YI + Y2 )!Y1Y1 (z, YI )!t;Y21 (y - Z,)12 )dY2dYldZ-00-00)'=- j'l

(8.37)

8.6.2 Point Crossing method

The general formulation given by (Eq. 8.37) involves triple integration and is usually hard

to evaluate numerically. The point-crossing formula replaces (Eq 8.37) by a simple upper

bound:

00 00

(8.38)

Where v[u} is the upcrossing rate for the process Y[t). For an important class of process

combinations, such as that one of the two processes Yj or Y2 has a discrete distribution, the

point-crossing formula represents an exact solution. More generally, it is exact if:

ply; (t) > 0 n Yj (t) < OJ= 0 (8.39)

Moatsos, I. 2005


For all processes i,j and all time t. This condition ensures that one process does not cancel

out the act of upcrossing of the other process by decreasing the value.

8.6.3 Load coincidencemethod

For the sum of two non-negative impulse type processes with the pulses returning to zero,

as shown in (Fig. 8.8) The load coincidence method, as it can be found in Wen (1977),

consists if calculating the upcrossing rate by considering upcrossings of each process acting

alone as well as upcrossing when the pulses of both processes overlap. The approximation is

given by:

(8.40)

, in which A.; is the mean pulse arrival rate of the process flt), J1j is the mean duration of the

pulses of flt), F/(y)=l-Fly) is the exceedance probability of threshold y, and F*12(Y)is the

exceedance probability of the coincidence process. The accuracy of the load coincidence

method, accoriding to Wen (1977) and (1990), is good regardless of the sparsity of the

processes, and is always on the conservative side. The method is applicable for linear

combinations of Poisson processes, intermittent processes, and pulse and intermittent

processes and can also be extended to the consideration of multiple load combinations, and

load dependencies including clustering within loads and also correlations within loads.

8.6.4 Ferry Borges Approach

The Ferry Borges approach, as it can be found in Ferry Borges & Castanheta (1971) and is

graphically illustrated in (Fig. 8.9), is a discrete process generated by a sequence fk of

independently and identically distributed random variables, each acting over a duration ti,

Due to independence, the distribution of the extreme value of the sequence in an interval

[O,T] is given by:

(8.41)

Moatsos, I.2005


If we consider two Borges processes YI and f2, as it is demonstrated in (Fig. 8.9), with

durations '/ and 12 respectively, where Tj/'2 is an integer, which is satisfied for more

practical applications when ti» '!2. Within the duration of ti, the maximum value of linear

combination of Y/ and Y2 can be expressed as:

(8.42)

which has the following cumulative distribution function:

T)

r;.....r(y) = r..fy) (v)[FY2 (y - v)r dv (8.43)

8.6.5 Peak Coincidence Approach

The peak coincidence method simply assumes that the maximum values of individual

processes will occur at' the same instant in time. Hence, the maximum value of

f(t) =L Y; (t) in a reference time period of T is given by:

(8.44)

which in most cases provides a conservative result.

8.6.6 Turkstra's Rule Approach

According to Turkstra (1970) and his approach, the maximum value of the sum of two

independent random processes occurs when one of the processes has its maximum value,

that is:

(8.45)

in which Y/ is the arbitrary-point-in-time value of lj. Typically, lj. is taken as the mean

value of lj. Although a simple and convenient rule for code calibration and some other

Moatsos, I. 2005


situations, Turkstra's rule may be a lower bound solution to load combination, and may thus

somewhat underestimate the maximum value.

8.6.7 SRSS Rule Approach

The square root of the sum of squares (SRSS) rule was originally proposed by Rosenblueth

et al. (1954), and has been used traditionally to combine the peaks of collinear modal

responses. In the case of a linear combination of the structure's independent modal

responses (i.e., modal frequencies are well separated):

(8.46)

where c, are constants, the root-mean-square (rms) value of yet) is a time period T

approximately follows:

~E[Y(TY] ::: (8.47)

Goodman et al. (1954), contend that the ratio between the maximum response and rms value

at time T is approximately the same for all the modal responses and for the combined

response, independent of their periods and frequency contents, i.e.:

E[Ymax]::: p~ E[Y(TY]

E[Xj,max]= P~E[Xi(T)2] i=I, ... ,n

(8.48)

(8.49)

in which the constant p is known as the peak factor. Hence, the expected maxima of the

combined response and of the modal responses are related by the SRSS rule as follows:

(8.50)

If the peak factors are not identical, the SRSS rule may then be easily extended to:

Moatsos, I.2005


(8.51)

It has been thought that the peak factor of the combined response may be considerably

larger than those of the modal responses, i.e., Pr » Px.» because the combined responseI

tends to have a larger bandwidth, according to Toro (1984). This implies that the SRSS rule

based on assuming an equal peak factor may considerably underestimate the combined

extreme response.

8.7 l\fodelling Slamming

According to Jensen & Mansour (2002), in the conceptual design phase an accurate estimate

of this parameter is needed to derive the necessary section modulus of the hull and usually

its value is taken from classification society rules where explicit formulas are given for the

hogging and sagging wave-induced bending moments. These depend only on the main

dimensions of the ship (length, breadth, block coefficient and sometimes bow flare and

forward speed) and the operational profile does not enter these expressions, with the vessel

modelled as a piece-wise prismatic beam (Fig. 8.10). The formulas are empirical in nature

relying strongly on past experience on hull failure together with a good engineering

judgement on the pertinent parameters. However, since the formulas do not depend on the

operational profile, the naval architect cannot asses the influence of e.g. a weather routing

system or speed reduction in heavy sea.

Direct ca1culation of the maximum wave-induced bending moment a ship may encounter

during its operational lifetime can be performed taking into account the hull form, mass

distribution and operational profile, according to Jensen & Mansour (2002). A linear

analysis is straightforward using either two or three dimensional hydrodynamic procedures

based on potential theory. However, the maximum values of the measured wave-induced

bending moment show significant non-linearities with respect to wave height, especially for

ships with fine forms and large bow flare. Thus the best way to approach such a problem

would be through the use of a non-linear procedure that will be able to capture such effects

Moatsos, I.2005


and that will take into account the stochastic nature of the sea necessitating a large number

of time domain simulations and a proper estimation of the extreme values.

Jensen & Mansour (2002) have suggested a rational procedure which is able to predict the

design wave-induced bending moment by taking into account parameters such as length,

breadth, draught, block coefficient, bow flare coefficient, forward speed and operational

profile. Non-linearities in the wave-induced response and whipping contributions are

included and the formulas derived are semi-analytical to provide ease of calculation thus

enabling the naval architect to estimate the wave-induced bending moment at the conceptual

design phase and to perform a sensitivity study of its value with respect to the pertinent

design parameters and the operational profile. Therefore the procedure can be useful in

reliability assessments of the hull girder where uncertainties in the strength and the

degradation due to wear and corrosion can be accounted for.

The effect of impulsive loads like slamming and green water on deck on the wave-induced

bending moment is estimated by a semi-analytical approach. The impulse loads leading to

transient vibrations are described on terms of magnitude, phase lag relative to the wave-

induced peak and decay rate. These loads can be due to bow flare slamming, bottom

slamming or green water loads as they all can be characterised by a short duration relative to

the wave cycle.

The frequency response function l/JM for the vertical wave-induced bending moment for a

homogeneously loaded box shape vessel can be derived analytically using the linear strip

theory proposed by Gerritsma and Beukelman (1964). Neglecting the small contribution

from hydrodynamic damping the result becomes according to Jensen (2001):

(8.52)

Here k is the wave number, lOthe wave frequency (oJ=kg) and L the length of the box. The

Smith correction factor Kis approximated by:

K === e:" (8.53)

Moatsos, I. 2005


, where T is the draught. The sectional added mass m; is assumed independent of OJ and

taken as equal to the displaced water:

(8.54)

such that lPM becomes:

(8.55)

with:

kL ..,n2q=-=/~~2

(8.56)

where:

(8.57)

Here A is the wave length and:

Tr=-L

(8.58)

It is evident that (Eq. 8.55) also holds for forward speeds greater than zero in case of a box-

shaped homogeneous loaded vessel. However for block coefficients Ci«l corrections factor

for speed V (or Froude Number Fn = ;;,) and block coefficient Cb need to be introduced.vgL _

A speed correction factor has been proposed by Sikora (1998) based mainly on naval ships:

Moatsos, I.2005


(8.59)

where Cv is given for different type of vessels and with V in knots. In this study the speed

dependence factor was taken as:

Fv (Fn) = 1+ 3Fn2 (8.60)

as it is found to be a better approximation of results from strip theory analyses performed

for a range of ship types. It also reflects that the low speed usually does not change

considerably the magnitude of the bending moment response. For ships with small block

coefficient Cs, the submerged volume of the fore part is especially reduced. This must result

in a lower bending moment as the wave-induced force in the fore part becomes smaller. In

order to get an estimate of this effect, a box shaped beam with two breadths Band B1 but the

same draught T along the whole length is considered. As it can clearly be seen in the

appendix (Fig 8.10) B JIB, a and Cb are related according to:

(8.61)

If the wave-induced loading on the vessel is assumed proportional to the breadth but

otherwise the same along the whole length, then the bending moment M amidships becomes

proportional to:

(8.62)

Assuming BJIB-O.6 as a representative value yields a reduction factor FCb(Cb) as shown in

(Table 8.1). As FcdCi) is a factor on the frequency response function it is, however, easy to

replace it with another one, reflecting better a specific type of ship. With this factor the peak

of the new frequency response function (Eq. 8.55) reduces to about O.018pgBL2 for Cb=O.6

and V=O. This is in agreement with most measurements and calculations for fine form ships

as represented in Sikora's empirical expression for the frequency response function,

according to Sikora (1998), but also reflects that the bending moment increase with Cb, as

Moatsos, I.2005


also stipulated in the formulas issued by the classification societies. However, the variations

of the block coefficient factors differ in as shown in (Fig. 8.11).

The standard deviation of the wave induced bending moment is given from:

s. = pgBL'H,F, (Fn)F",(C. )/.(T' ~ Llc!sP\ Jl{ 4Jr

2T~g }3(~)cOS~~

(8.63)

The skewness of the response is the most important statistical moment for the

sagginglhogging ratio for the wave induced bending moment and also, albeit together with

the kurtosis, for non-linear behaviour in general. For the sagging bending moment the

kurtosis is less important as its effect on increasing the moment is much less than that of the

skewness (Vinje & Haver, 1994). For the hogging bending moment the situation is different

as the skewness and kurtosis here counteract each other for the wave induced bending

moments. The result is typically that the non-linear hogging moment peaks become slightly

lower than the linear prediction (Jensen & Pedersen, 1979). An examination of the results

for the skewness k3 reveals that it changes with heading p and Froude number Fn according

to:

[ (-1OFn]J (T -5 )k3 =O.26H se f 1- exp IcosPI min ~ ,1 (8.64)

For the kurtosis there is not a useful analytical expression that can be used (Jensen &

Mansour, 2(02) and as the kurtosis only has a relative small influence on the sagging

response the non-linear response is based on the skewness only and no non-linearities are

included in the hogging response, but according to (Jensen & Pedersen, 1979) these non-

linearities tend to reduce the hogging response to a lesser extend of 10-15%. The wave

induced bending moment then becomes accordingly:

(8.65)

Moatsos, l.2005


where U is a standard normal process and:

(8.66)

which holds is sag as k3>O but for hogging responses the expression cannot be used as k3<O

yields a non-monotonic transformation.

Whipping is then modelled as a stochastic process resulting from the water impact on the

bow and its magnitude of contribution to the bending moment amidships expected to be of

the order:

M wh QC L2pBs~, (8.67)

where L2 accounts for the lever and longitudinal extend of the force and SVr is the standard

deviation of the relative vertical velocity at the bow. This term is typically given in non

dimensional form as:

(8.68)

where TJ depends on the operational profile and to some extent also on ship geometry. If this

variation is ignored then:

M wh QC pgBLH; (8.69)

The quadratic variation with HS is in agreement with observation made by (Ochi & Bolton,

1973) & (Sikora, 1998) that the whipping response is exponentially distributed. Then from

(Eq. 8.69) the standard deviation may be written as:

(8.70)

Moatsos, I.2005


which is expected to increase with bow flare as the load is related to the impulse generated

when a section re-enters water. It should be noted in this point that the more slowly varying

momentum force related to the change of added mass during immersion is taken into

account in the skewness. Both the whipping and the skewness are assumed hence to be

proportional to the bow flare but with time variations of these load components being very

different. The whipping load is also assumed to be inversely proportional to the block

coefficient to reflect that full-form ships structures, like FPSOs, experience less whipping,

which leads to:

(8.71)

For the estimation of the Jl value the ratio between the standard deviations of the whipping

and wave-induced bending moment can be used:

2 c,JlpgBLHs - C

_S,,_'h = Cb :::;:300Hs _I J10.0033pgBLH; L c, (8.72)

where the number 0.0033 corresponds to the maximum standard deviation using the Sikora

(1998) frequency response function, without speed effect and in head seas. If this ratio is

known from simulations or model tests in a specific sea state, J1 can then be estimated.

Typical values are expected to be in the range of 0.02-0.05 but it should also be noted that

the ratio between the extreme values of the two responses is larger than the ratio:

Swh InN swh fi N 10-=r===>- or ~SM .J21nN SM

(8.73)

The hull girder stiffness does not influence (Eq. 8.71) as its main influence is on the

vibration frequency and decay rate. A detailed description of the procedure can be found in

Jensen and Mansour (2002) and has been extended in Jensen and Mansour (2003) to cover

more in detail the whipping contribution

Moatsos, I.2005


8.8 lACS Loading

If reliable measure of ship safety is to be established, the accuracy in load determination

must match that of capability. In recent years much experience has been gained on the

subject of wave-induced loads, as it can be seen from the previous sections of this chapter

and the review of some of the available literature in (Chapter 3), and the magnitudes now

thought to be appropriate for design are higher than those used in the past. The International

Association of Classification Societies (lACS) has agreed on a unified longitudinal strength

standard (lACS, 1989), (lACS, 2003) where the midship wave-induced bending moments

are defined as follows:

In Hogging: (8.74)

In Sagging: (8.75)

where B is the greatest moulded breadth in meters, L is the length of the ship in meters, Cs

the block coefficient and the coefficient C is given from:

C=1O.75-[(3~~L)r for 90'; L'; 300

C = 10.75 for 300 < L < 350

C = 1O.75__ [(L-350)]1.5 for 50:C:;L:C:; 500150

(8.75)

lACS also gives the following recommendations for the minimum design midship still-

water bending moments M.rw:

In Hogging: (8.76)

In Sagging: (8.77)

The rules also state that larger values based on load conditions are to be applied when

relevant.

Moatsos, I.2005


8.9 Approach

8.9.1 Introduction

For the wave-induced short term loading, St. Denis & Pierson (1974) accomplished the

extension of regular wave results to predicting ship responses to short-crested irregular seas,

on the assumption that both the irregular waves and the short-term responses are stationary

stochastic processes. The response of a ship in irregular waves can be taken as the

summation of the individual response to the regular waves, which form the confused sea.

By short-term is meant periods of typically a few hours during which sea conditions remain

essentially constant. Hence under these assumptions, the bending moment response can be

predicted for any ship for which transfer functions are available. The square of the transfer

functions are called response amplitude operators (RAO) and they can be multiplied by the

directional wave spectra to produce the directional response spectra:

SB (OJ, Ii) = S; (OJ, Ii ) ·1<1> (OJ, u~2 (8.78)

where SB is the bending spectrum given by the product of the non-linear transfer function t:/J

for a specified relative heading and significant wave height (RAO), and the seaway

spectrum S;. When these components are integrated over the wave direction a single

response spectrum is obtained, whose area and shape define the bending moment response:

(8.79)

Short terms statistics can be derived from the response spectrum by taking the various

moments SB( OJ),

(8.80)

For the modelling of the response the variance is of special interest and is given by:

Moatsos, I.2005


(8.81)

The fundamental assumption in this approach is that the wave induced stresses are a linear

function of suitably defined wave elevations and that the response spectrum may be

estimated using a computer code or model tests. A consequence of this assumption is that

the wave-induced stresses must be a zero mean random Gaussian process. A further

consequence is that the process must be statistically symmetrical. That is, the short term

statistics for the wave induced bending moment maxima in hogging are assume the same as

for sagging.

For a broad-banded response spectrum, the Rayleigh distribution in not immediately

applicable and a more generalised distribution, involving the spectrum broadness parameter

C, is required. The statistics of a broad-banded response are different in many respects from

those of a narrow banded spectrum having the same ma and rn2. Nevertheless Ochi (1973)

showed that the most probable extreme value and the mean extreme value are still

theoretically predicted by the narrow band formulae. Dalzell et al. (1979) proved that for a

slow, ocean going ship with with C» (such as 0.84), a Rayleigh distribution is an adequate

statistical description of the short-term response amplitudes of bending moment.

A number of long-term prediction procedures have been proposed (Lewis, 1957).

(Norden strom. 1971) & (Guedes Soares, 1984) for the bending moment response estimation

for any ship, with several assumptions, for which transfer functions are available. The

method used to define suitable sea spectra was the ISSC version of the Pierson-Moskowitz

spectrum given by Wamsick (1964),

(8.82)

where Tm is the average period and H, is the significant wave height. Having the Response

Amplitude Operators (RAOs), the bending moment response spectra can be calculated by

superposition for all of the selected wave spectra. The directional spectrum represents the

distribution of wave energy both in frequency of the wave components and in direction. B.

Moatsos, I.2005


The analysis of directional buoy records has shown that the spreading function is function

of both direction and frequency. Pierson and St. Denis used a directional spreading function

that became somewhat generalised because of its simplicity. It is a frequency independent

formulation given by:

G(8)=O

(8.83)2G(8)=-cos28n

(8.84)

where 8 is the angle between an angular wave component and the dominant wave direction.

The short-term responses were combined with long-term wave statistics to determine the

long-term probability of exceedance of different wave induced vertical bending moments. A

Weibull distribution was fitted to the resulting distribution. The rationally based design of

ships requires the consideration of the largest value (extreme value) of the wave loading,

especially the wave-induced bending moment, which is expected to occur within the ship's

lifetime. The prediction of the characteristic value, which is associated with a certain

probability of non-exceedance in the time, is of particular interest. The characteristic value

is that magnitude of extreme value, which has an appropriate probability of exceedance.

There are usually good theoretical grounds for expecting the variable to have a distribution

function, which is very close to one of the asymptotic extreme-value distributions. It has

been shown that the extreme Vertical Wave Bending Moment (VWBM) can be described

by a Type I extreme-value distribution, generally called Gumbel distribution:

FGumb (M ~)= exp[-exp(-a(M ~ -u))] (8.85)

Guedes Soares (1984) showed that the Gumbel parameters can be estimated from the initial

Weibull fit using the following equations:

(8.86) (8.87)

where nw is the number of peaks counted in the period T; given by:

Moatsos, I.2005


Tn =_cw ~

(8.88)

which is the average mean zero crossing periods of waves. The parameters Uw and aware

respectively measures of location and dispersion and Uw is the mode of the asymptotic

extreme-value distribution, k and b are the Weibull scale and shape parameters. The mean

and standard deviation of the Gumbel distribution is related to the Uw and aw parameters as

follows:

(8.89) (8.90)

where 'Y is Euler's constant equal to 0.5772.

Considering only the still water induced and wave induced components of the hull girder

loads independently and by using the Ferry Borges-Castanheta load combination method

(Ferry Borges, & Castanheta, 1971), the load combination factor, 'I'w, for the deep condition

can be obtained. As the still water and wave bending moments are stochastic process, the

maximum SWBM and VWBM do not necessarily occur simultaneously in a ship's service

lifetime. Moan and Jiao (1988) considered both SWBM and VWBM as stochastic process,

and, based on a particular solution by Larrabee & Cornell (1981) they introduced a load

combination factor, derived by the combination of two stochastic processes:

M le =M"", + fjIswM se= fjI wM we +M see (8.91)

where 'P'swand 'P'ware load combination factors, while Mse and Mwe are the extremes of the

still-water and wave induced bending moments.

8.9.2 Ferry Borges-Castanheta :Method

The method simplifies the loading process in such a way that the mathematical problems

connected with estimating the distribution function of the maximum value of a sum of

loading process are avoided by assuming that the loading changes intensity after a

Moatsos, I.2005


prescribed deterministic, equal time interval, during which they remam constant. The

intensity of the loads in the different elementary time intervals is an outcome of identically

distributed and mutually independent variables. A time interval for still-water loads would

typically be one voyage for a conventional ship. For a production ship, the period between

different loading conditions must be defined from the operational profile.

In the method, the point-in-time distribution for load process {x} is defined as !xi (densityfunction) and the corresponding distribution function is Fxi. The cumulative distribution

function of the maximum value in the reference period T is then given by (Fxiti, i.e.:

(8.92)

From load combination theory, we have that the density functions are determined by the

convolution integral:

00

fZi+Zj (x)= JIZi (z}/zj (x- z}lz (8.93)

and from basic statistics we have

00

FZji (x)= flzi (z).dz (8.94)

By combining (Eq. 8.92), (Eq. 8.93) & CEq.8.94) we end up with the following expression:

00

FImX.z,+Zj(x)={ flzj (z}.[FZ;(x- zWj d; }nj (8.95)

Taking Xi and Xj as Msw and M; respectively, (Eq, 8.95) may be applied directly to the

combination of still water and wave induced bending moments. The total vertical bending

moment, Mt. may then be estimated by:

Moatsos, I. 2005


(8.96)

The density distribution functionji; is the still-water bending moment in one year, which is

a normal distribution. The number of occurrences of each load condition, nsw, is defined by

the operation profile. [Fw]nw is the Gumbel distribution of the extreme wave induced

bending moment in one load condition derived from the Weibull distribution assuming nw

wave loads in each load condition.

Jn =~... J ...

(8.97)

Introducing a load combination factor, the total load might be defined as:

(8.98)

where the extreme distributions are considered at 0.5 exceedance level. The load

combination factor can then be determined by the following relationship:

F,-t (0.5)- F;:; (0.5)'1'... = F;I(O.5) (8.90)


8.10.1 Comparing the Load Combination Methods

As a starting point for the loading analysis of this study, as it is quite evident from the

theory that has been examined so far, the best way for combining SWBM and VWBM using

different stochastic and deterministic methods needed to be examined. All the different

approaches theoretically examined so far, were mathematically modelled in Mathcad

Version 12.0 developed by Mathsoft. The sagging condition for one of the FPSOs was

examined and using the design SBWM and VWBM according to the IACS (IACS, 2003)

recommendations the long term distribution of the VWBM and SWBM was determined

according to (Section 8.4) using a design life period of 20 years corresponding to a total

Moatsos, I. 2005


number of 108 wave cycles. The mean period of a still water load condition was taken as

l/vs=lday. This corresponds to the average duration of the still-water load condition for

such type of vessel. As it can be seen in (Moan & Jiao, 1988) & (Wang & Moan, 1995) the

load combination factors are not sensitive to a variation of l/v, in the range from several

hours to a few days. Load combination factors using all the approaches were calculated and

the results can be seen in (Table 8.3). Assuming that the exact solution is provided by the

point-crossing method, the differences between the methods were calculated. From the

methods compared the other stochastic models, namely, the load coincidence method, the

Ferry Borges method and the solution by Moan & Jiao (Wang & Moan, 1995) & (Moan &

Jiao, 1988), all resulted in very close and similar results, indicating that although such type

of analysis and approach might have originally been developed for use in other types of

problems combining various types of loading, not necessarily in marine structures, can be

very accurate and suitable for application in the combination of SBWM & VWBM in FPSO

structures. In addition to this, as expected, the peak coincidence method is very conservative

with an over-prediction of the maximum total moment by 24%. The other deterministic

models are all nonconservative, with the solution by Soding (1979) giving the smallest

deviation of 2.3%. The approach by Turkstra ·(1970) giving a deviation of 8.3% and the

SRSS rule (Goodman et al., 1954) is the most divergent with a difference of 9.4%. All of

the results calculated were based on the assumption that the peak wave moments of each

cycle are mutually uncorrelated.

8.10.2 Calculated Loading

Applying the lACS formulation described in (Section 8.8) of this chapter to the 3 FPSO

structures provided the minimum design midship sti1l-water bending moment values and the

minimum design midship wave-induced bending moments as summarised in (Table 8.4).

All these values were used throughout the analysis to either specify mean values or starting

values for the methods used, as discussed in all the previous sections of this chapter. They

formed a basis for comparison to the results obtained when slamming effects were taken

into account and as "ballpark figures" to ensure that the calculations were of the correct

magnitude.

The prediction of the still-water load effects raises no difficulties once the loading

procedures of the vessel are specified. In this case the primary hull structure is modelled as

Moatsos, I.2005


a beam and the load effects are determined by integration over the length of the ship. This

can readily be done in a number of computer packages. In determining the design value of

the still-water load-effects, several representative load conditions must be considered. The

reference value adopted for deterministic design is the maximum that occurs in these

conditions or the minimum design requirement for Classification Societies' Rules,

whichever is greater. In a reliability-based analysis, the SWBM for each condition is taken

as the mean or characteristic value, and an uncertainty is assigned. The SWBM for each

loading condition were calculated using Autohydro computer code which is part of the

Autoship suite of programs developed by the Autoship Systems Corp. and that is used by

the Dept. of Naval Architecture and Marine Engineering of the Universities of Glasgow and

Strathclyde. The main input to the program for one of the FPSOs analysed can be seen in

(Fig. 8.12) for the weight distribution, (Fig. 8.13) for the offsets and (Fig. 8.14) for the hull

geometry model. The longitudinal loads in the hull girder were calculated and the

characteristic values of the SWBM were taken as the highest value in each loading

condition (Table 8.5).

The operational profile for the vessels was provided for two of the FPSOs from Shell UK,

Exploration & Production but in some cases no operational profile was available at all. A

simplified operational profile was used in these cases based on the production and storage

capacities and a rectangular pulse process was fitted. The operational procedures and

profiles used were described in (Chapter 4) and can be seen in (Table 4.5). The assumed

operational profile can also be seen in (Fig. 8.15). Then the extreme model (Section 8.4)

was applied for each of the load conditions to obtain all the short-term and long-term

required for reliability analysis. As an example of the results obtained for the TRITON

FPSO, (Fig. 8.16) illustrates the Gumbel probability density function of the extreme SWBM

for the loading conditions and (Fig. 8.17) the distribution function for the extreme SWBM

again for all the loading conditions analysed. The extreme SWBM caluclatn were carried

out as part of the load combination factor calculation and (Table 8.5) gives a summery of

the extreme values of the SWBM obtained for the FPSOs analysed. The differences

between the sagging and hogging extreme values are quite significant, keeping in mind the

sign convention, positive values for hogging and negative values for sagging. In hogging the

wave load and SWBM will have the same sign, both will give hogging moments, whereas in

sagging there will be a hogging SWBM and a sagging VWBM. This is a very significant

factor when considering the reliability of the vessel in (Chapter 9).

Moatsos, I. 2005


For the calculations of the transfer functions of the FPSOs analysed the WASIM code

developed by DNV (DNV, 2003) which forms part of the SESAM suite of programs.

WASIM is a program for computing global responses and local loading of vessels moving

at forward or no speed, as long as the vessel is not planning. A detailed description of the

theory used by the code can be found in (DNV, 2003) and is not described in detail in this

thesis as it falls beyond the scope of this study. Nevertheless the approach used is briefly

commented upon in (Chapter 10). The wave load analysis was performed for all operating

conditions and the ship was assumed moored and free to weathervane within +/- 3rJ' fromthe predominant wave direction. The wave induced response serves as input to the post

processing code that calculates the long-term distribution of the VWBM. The transfer

functions for one of the FPSOs analysed can be seen in (Fig. 8.18)

A FORTRAN 90 code was developed to calculate the probability distribution of the wave

induced load effects that occur during-long term operation of the ship and a flow chart of

the procedure can be seen in (Fig. 8.19). The code reads the RAOs for the vessel analysed

and the data from the scatter diagram from data files. The RAOs are given in a non-

dimensionalised form, so all the values obtained have to be multiplied by pgaBL2 in order to

get consistency in the calculations. Then the code calculates the average rna for 7 different

ship headings, and then calculates the probability for exceeding a value of the VWBM, for

this particular combination of wave height, wave period, ship speed and load condition. A

summation of rna over 11 T; and 15 H, is then performed in order to obtain the total

probability of exceeding amplitude x. As described in (Section 8.5) ship and speed load

conditions are taken into account by assuming constant speed and performing calculations

for different conditions. The calculations for Q(x> VWBM) is done for 12 values of VWBM,

from 500MNm up to 6000 MNm and the results are written in an output file.

The long-term prediction of wave induced bending moments has taken into account the

actual environment that the FPSOs have been operating. From its nature the FPSO is a

stationary vessel and a site-specific analysis is required. In our case for all the FPSOs

analysed, Area 11 of the Global Wave Statistics (Hogben et al., 1987) were used.

Measurements of the directional spectrum at the site over many years would have been the

preferred basis for the wave statistical analysis but unfortunately very few sites where

Moatsos, I.2005


spectra are available for a minimum of 2-5 years exist in the published literature and hence

the Global Wave Statistics are widely used for design purposes. The long-term distribution

for the Full Load of the Schiehallion FPSO can be seen in (Fig. 8.20) according to the

theory described in (Section 8.5) & (Section 8.9). As this is a non-linear analysis, no

distinction is made in this stage between hogging and sagging moments. The effect of non-

linearity is incorporated by introducing a correction factor Xnl in reliability analysis (Chapter

9).

For the slamming calculations, a modified version of the "Probabilistic Design Loads"

(PRODEL) code developed for MS Excel by Dr. J.J. Jensen was used, after obtaining his

permission. The code calculates the standard deviation, the peak value distribution and, if

requested, the combined wave-induced and whipping bending moment response according

to the theory described in (Section 8.6) of this chapter. The long-term response is also

calculated applying the user-defined operational profile of the vessel and a Weibull fitting

of the response is performed. The coefficients in the Wei bull distribution are obtained

through a Visual Basic code utilising the SOLVER option that MS Excel has as standard.

The results of the analysis using a scatter diagram for the actual area of FPSO operations

can be found in (Fig. 8.21) showing the non-linear long-term probability of exceedance and

(Table 8.6) showing the comparative results obtained for the Anassuria FPSO, (Fig. 8.22)

and (Table 8.7) for the Schiehallion FPSO and (Fig. 8.23) and (Table 8.8) for Triton FPSO.

The load combination factors were calculated for the three loading conditions, based on the

operational profile and extreme loads and for all conditions in all events considered

(different locations, different load models etc). These calculations form part of the basis of

the reliability analysis. As an example, the cumulative distribution functions for the

individual loads and the combine effect can be seen in (Fig. 8.24), (Fig. 8.25) and (Fig.

8.26) for the Full Load, Partial Load and Ballast Load conditions respectively. The values of

particular interest to our analysis for the load combination are the VBMs that have exactly

50% probability of being exceeded. These can be found in Tabulated form for all of the

FPSOs in (Table 8.9).

Hydrostatic pressure acting on the side shell Will induce transverse stresses in the bottom

plating as well as local bending stresses in the side shell. As the hull strength programs that

Moatsos, I.2005


were used to validate the MUSACT code developed for the determination of the US of the

hull girder were restricted to the application of bending loads alone, these additional

components were not taken into account. These additional components need to be

incorporated where necessary by adjusting the uni-axial stress data. Furthermore, as stated

in previous sections of this chpater, transverse stress in the bottom structure resulting from

pressure on the side shell have been estimated to be approximately 4% of the yield stress for

tanker type structures according to Rutherford & Caldwell (1990). This level of stress will

have a negligible influence on the axial-carrying capacity of the structure and has therefore

been ignored. Overall bending of the bottom structure between bulkheads and girders has

been similarly ignored on the basis that the resulting longitudinal plating tension in the

vicinity of these members will be counteracted by compression in the remaining structure.

Lateral pressure effects on a local level considered in the analysis are therefore restricted to:




strain data. Slamming effects are treated separately and combined with the overall loading

as described in (Chapter 8) of this thesis.

The transfer functions calculated usmg the WASIM Code were obtained through

simulations in the time domain but results are also transformed in to the frequency domain

by using Fourier transforms. The code used solved the fully 3-dimensional

radiation/diffraction problem by a Rankine panel method. For these methods panels are

required both on the hull and on the free surface. The current version of the code only

supports transfer of normal pressures for the linear option and in this case the pressures are

transferred in frequency domain. Also a number of non-linear effects were included during

the non-linear analysis:

• Integration of Froude-Krylov and hydrostatic pressure over exact wetted surface.

• Quadratic terms in the Bernoulli equation are included.

• Exact treatment of rotation angles in inertia and gravity terms.

• Quadratic roll damping.

Moatsos, I.200S


With the non-linear option, the radiation/diffraction problem is also solved on the mean free

surface and mean wetted surface.

Moatsos, I. 2005



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Moatsos, I. 2005


Appendix 8, Figures

eNS

I

Il

I • Maximum WayeHeight

.Peak Period

t 1 .Significant Wav.

I Height

NNS

SNS

~ H ~Wave Height [m] I Peak Period lseesl

Figure 8.1 Typical Extreme (100yr) Wave Heights, (IMarEST, 2004).

N

w

s

Figure 8.2 Central North Sea wind speeds (mls), (IMarEST, 2004).

Figure 8.3 FPSO Wind Tunnel testing, (The Naval Architect, 2004)

Moatsos, 1. 2005


SWBM

T

Figure 8.4 Modelling of SWBM by a Poisson rectangular pulse process.

Il.. '.00U

0 ••

0••

0••

0 ••

0.0a au

__ eet1IIIIl CDF

___fitt" byl •• ", COF

10 ea ea .aoBEND ING MOMENT

Figure 8.5 Sagging SWBM distribution in production ship, (Moand & Jiao, 1988)

140- w..buI approx. ~ seas_--- w..buI approa. short-c:resttld seas• 0ir8d summalicII\ ~ ...o Onct summatiOn short-ct8SUld __:t20

!.• tOO1:: 80rc 60••! 40o

20

O+---~--r-~~~~~---T-'-T~-r~~~ ~ ~ ~ 4 4 4 ~ ~ 0

logOFigure 8.6 Long-term distribution of deck stresses resulting from VWBM, (Frieze et al., 1991)

Moatsos, I. 2005


clumping

~Realization of X({)

"~ \

I I

" ':

Figure 8.7 Realization of process X(t) showing clumping effect and barrier crossing.

T

.......Strct)

Figure 8.8 Load coincidence for rectangular pulse processes, (Wen 1990).

tl

Figure 8.9 Ferry Borges Processes

!

.J

Moatsos, I. 2005


iJJJ-d~

I t-~ I. l

~

.ru..

~

2I Tt I·

~

:]8, le :Figure 8.10 Piece-wise prismatic beam

1f-FCb(Cb): 81/8=0.6'I-IAC$-sag

0.9 ::_--~-".~-,-

0.8

0.7

0.60.6 0.7 0.8 0.9 1

Figure 8.11 Assumed variation of bending moment with block coefficient (Jensen & Mansour, 2002).

5000, -e-Fuli Load

4500 __ ParlialLoad

4000 -6-Ballasl Load

3500

iii 3000~:.eCl 2500..s

2000

15001I1000 i•I

500'

...... '1>'1;>.. ~ ... '). .. 'b~~'1> ,\'00,.'" t§>'?'" ~tf> -voJ> ......<;>" ,,}' ..... 0/ n,'O~ ~~ '\ -,~ ~ ~ -c~~

Longitudinal location of point weights (m)

Figure 8.12 FPSO Triton weight distrubution for various loading conditions.

Moatsos, I.2005


gs:i 10.0c

15.0

5.0

0.021.0 18.0 15.0 12.0 9.0 6.0 3.0 0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0

Breadth (m)

Figure 8.13 Triton FPSO cross-sectional offsets.

Figure 8.14 Triton FPSO hull geometry model in Autohydro.

Moatsos, I. 2005


Full Load

Partial Load

Sdays ...24 h.< ,,( 72h. 24h.

)( )

-,,,,-,,,,

-,,,,,,,,,J.,',,,

I,,,..__ I

I II ~

po~-~

,.1" I'

"

,,,,, ",,,

/1'11•• " ... Load L..j I I

I

,,

IL------. Assumed Load Process- Simplified Load Process

Figure 8.15 Assumed operational profile fitted as a pulse process.

0.0071

0.006

0.005

-; 0.004::I!

J0.003

0.002

0.001

00

I -FuUload

__ Ballast load

-- Partial load

r--··~·--'1

500 1000 1500 2000 2500 3000 3500 4000 4500

Figure 8.16 The extreme SWBM probability density functions for 3loading conditions (Triton FPSO).

M_(MNm)

Moatsos, I.2005


1.00 r------:ii"'------~-.------.....-....,0.90

0.80

0.70 ,__._J__-Full load,-- Ballast load1--Partial load

I

0.60 1i. 0.50.110. 0.40

~:: 11

0.10

0.00 .......--~o 500 1000 1500 2000 2500 3000 3500 4000

M.(MNm)

Figure S.17 The extreme SWBM probability distribution function Cor 310ading conditions (TritonFPSO).

0.02

:..11:1Cl..0..

I0.0151

I0.01 1

!

-6-0·

-6-30·

-e-eo·--90'

-+-120·

-H-150·

0.2 0.• 0.11 1.2 1.•

Ie.e.. 1

o l···o 0.11

Frequency (redl.)

Figure S.18 Transfer functions Cor Triton FPSO Cor Cull load condition.

Moatsos, I. 2005


I Start J~.

Read Data from filesRAO.res, frequency.dat

and scatter.dat

1.. Calculate Q(x) for 12 different

Vertical Bending Moments

!Summation ofQ(x) over the Scatter Diagram

(llx15 entries)

+Calculate average moover 7 Ship Headings

+.. Calculate the Pierson-Moskowitz

Wave Spectrum for 19 frequencies

~

Calculate the Directional Response Spectrum

~Calculate mo. by integrating theDirectional Response Spectrum

+Calculate Q(x)

~Write Q(x) and VBMto the file Output.res

~Stop

JFigure 8.19 Algorithm for the calculation of the long-term probability distribution of wave induced load

effects.

Moatsos, I. 2005


EZ YBMn

6+++ 200~ YBMn

>-

350

300

250

[00

50

oL-___L ~ __~ _L L_ __ ~ ~ L_ __ _L __ ~~

['10-10 ['10-9 1'10-8 1.10-7 1'10-6 ['10-5 1'10-4 ['[0-3 O.O[ 0.1Qx.,, Weibulln

Q(x)

Figure 8.20 Long-term WeibuUfit distribution of the vertical bending moments for Schiehallion FPSO.

Non-linear long tenn probability of exceedance for individual sag peakvalues (new AAO and Sikoras)

-- Numerical integration

--Weibull: Scale (MNm): 89.1 Exponent: 0.7176

- - - .num. integration using Sikora's RAO1 .E+OO -r---===~====:::::;=====::::;:::=====::;::=====;:======;======:;::===:_'1.E-01

1.E-06

1.E-07 -

1.E-08

1.E-09 -

1.E-101.E-11 .L, .....J

1.E-02

1.E-03

1.E-04 -

1.E-OS

1000 3000 4000 5000 6000 7000MNm

8 02000

Figure 8.21 Anassuria FPSO non-linear long-term probability of exceedance.

Moatsos, I. 2005


Non-linear long term probability of exceedance for individual sag peakvalues (new RAO and Sikoras)

- Numerical integration


- ••. num. integration using Sikora's RAO

1.E+OO -.-----===:::;=====:;:::====:;:::====:::;:::====::;::====~====~==:::-_,1.E-01

1.E-02

1.E-Q3

1.E-04

1.E-OS

1.E-06

1.E-07

1.E-08

1.E-Q9

1.E-10

1.E-111.E-12 .L ~_~

1000 2000 3000 5000 6000 7000MNm

8

1.E+OO -.-----===::;:=====::;:::=====;::====:::;::=====:::;:====:::::::;======;::::==~1.E-01

1.E-02

1.E-03

1.E-04

1.E-OS

4000..

Figure 8.22 Schiehallion FPSO non-linear long-term probability of exceedance.

Non-linear long term probability of exceedance for individual sag peakvalues (new RAO and Sikoras)

-- Numerical. integration


- • - . num. integration using Sikora's RAO

8 0

1.E-06

1.E-07

1.E-08

1.E-09

1.E-101.E-11 ..1- __1

3000 5000 6000 7000MNm

Moatsos, I. 2005

40001000 2000

.. .. .. .. .. .. .. .. .... ...... .... .. "... ".

Figure 8.23 Triton FPSO non-linear long-term probability of exceedance.


1.0010.90

0.801

0.70

0.60 .

0.50 t-! ---I------_,I---l

;=10.10 ~

0.00 L-- ..o 1000 2000 3000

I =:::~i -Fte,FL

VBM (MNm)

4000

Figure 8.24 Load distribution functions CorTriton FPSO in Full Load Condition.

1.00

0.90

0.80

0.70

- 0.60:::!:CO 0.50~K 040U.

0.30

0.20 ~

0.10

0.000 1000 2000 3000 4000

I-':"'_Fwe. PL__ Fse.PL

! -Fte.PL

sooo 6000

VBM (MNm)

Figure 8.2S Load distribution functions CorTriton FPSO in Partial Load Condition.

1.00 10.90

0.8010.70 I

i" 0.60

aI 0.50~..0.40U-

0.30 j

''10.10

0.00 .'-'-0 1000 2000 3000 4000

r

--::;.. Fwe,BL -.

__ Fse.BL

-FIe,BL

5000 6000

VBM(MNm)

Figure 8.26 Load distribution functions CorTriton FPSO in Ballast Load Condition.

Moatsos, I.2005


Appendix 8, Tables

Coefficient/Condition Intact Grounding Collision

Hogging ksw 1.0 1.1 1.0kw 1.0 0.5 0.7

Sagging ksw 1.0 0.9 1.0kw 1.0 0.5 0.7

Table 8.1 Load combination factors for still water and wave-induced bending moments.

A0.99 ...0.750.500.25

0.60.70.80.9

0.6000.6250.7000.825

Table 8.2 Block Coefficient Factor Fcb(Cb)

Sag ging Load Com binatio n Factors by 0 iffere nt M ode Is T0=20 Years

Model lI'w

Peak 1.0coincide nee

Turkstra's 0.59

SRSS Rule 0.57

Soding 0.66

Ferry Borges 0.69Method

Moan &Jiao 0.69

Point Crossing 0.69Method

Load 0.69coincide nceMethod

Table 8.3 Sagging load combination factor comparison using different models.

Moatsos, I.2005


FPSO TotalsHogging Sagging Hogging Saggingu.; Mw u.; MwMNm MNm MNm MNm MNm MNm

TRITON 2577 3447 2238 3787 6025 6025ANASSURIA 2496 4220 2494 4221 6716 6716SCHIEHALLION 2592 4122 2494 4220 6714 6714

Table 8.4 lACS Requirements for wave and still water bending moments.

Characteristic ValuesTriton Anassuria Schiehallion

Full 57517 564 55740 547 56381 553Partial 147971 1452 143399 1407 145050 1423Ballast 234425 2300 227181 2229 229797 2255

tonne-m MNm tonne-m MNm tonne-m MNm

Extreme ValuesTriton Anassuria Schiehallion

IJow a.w IJoo a.. IJow a.w 110. a.. IJow a.w I10e a..Hogging

Full 564 84.6 770 42.4 547 82 746 41 553 83 755 42Partial 1452 218 1982 109.3 1407 211 1921 106 1423 214 1943 107Ballast 2300 345 3139 173.1 2229 334 3042 168 2255 338 3077 170

Sagging .Full 564 85 358 42.4 547 82 347 41 553 83 351 42

Partial 1452 218 922 109.3 1407 211 894 106 1423 214 904 107Ballast 2300 345 1461 173.1 2229 334 1416 168 2255 338 1432 170

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm. .Table 8.5 Characteristic and extreme values of the SWBM for 3 FPSOs analysed •

Main results for most probable largest bendil'!9_moment (MNm) amidshipsCt: 0.25 Bow flare ext: 0.005 Green w. ext.: 0 Non-lin new

Rule Rule (ON\,) Linear New Linear Sikora Non-lin. New short-crestedSag 4221 5066 3596 3584 5059 4553

HOQ 4220 4220 3596 3584 3596 3237SaQ/hoQ 1.00 1.20 1.41Sag/Rule 0.85 0.85 1.20 1.08Sag/ONV 0.71 0.71 1.00 0.90

Hog/Rule 0.85 0.85 0.85 0.77. . .Table 8.6 Anassurra FPSO comparative results for bending moment including the effect of slanumng .

Main results for most probable largest bendin_g_moment (MNm) amidshi~sCf: 0.25 Bow flare ext: 0.005 Green w. ext.: 0 Non-lin new

Rule Rule (ONV) Linear New Linear Sikora Non-lin. New short-crestedSag 4220 5064 2713 3699 3945 3550

Hog 4122 4122 2713 3699 2713 2442Sag/hog 1.02 1.23 1.45Sag/Rule 0.64 0.88 0.93 0.84Sag/ONV 0.54 0.73 0.78 0.70

Hog/Rule 0.66 0.90 0.66 0.59Table 8.7 Schiehallion FPSO comparative results for bending moment including the effect ofslanumng.

Moatsos, I. 2005


Main results for most probable largest bending moment (MNm) amidshipset: 0.25 Bow flare ext: 0.005 Green w. ext.: 0 Non-lin new

Rule Rule (DNV) Linear New Linear Sikora Non-lin. New short-crestedSag 4247 5097 4505 3593 6062 5456

HO(! 4243 4243 4505 3593 4505 4054SaQ/hoQ 1.00 1.20 1.35Sag/Rule 1.06 0.85 1.43 1.28SaglDNV 0.88 0.70 1.19 1.07

Hog/Rule 1.06 0.85 1.06 0.96

Table 8.8 Triton FPSO comparative results for bending moment including the effect of siammmg.

Load Combination FactorsTriton Anassuria Schiehallion

M... (O.5) M.. (O.5) Mt(O.5) 'I'w M.w(O.5) Mw(O.5) Mt(O.5) 'I'w M.w(O.5) Mw(O.S) Mt(O.S) 'I'w

HoggingFull 763 2319 2882 0.91 739 2247 2793 0.88 748 2273 2825 0.92

Partial 1964 2500 4065 0.84 1903 2423 3939 0.81 1925 2451 3985 0.85

Ballast 3111 2251 4859 0.84 3015 2181 4709 0.81 3050 2207 4763 0.85

SaggingFull -365 2319 1754 0.91 -354 2247 1700 0.88 -358 2273 1719 0.92

Partial -940 2500 1162 0.84 -911 2423 1126 0.81 -921 2451 1139 0.85

Ballast -1490 2251 259 0.78 -1444 2181 251 0.76 -1461 2207 254 0.79

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

Table 8.9 VBM values with 0.5 level of exceedance and equivalent load combination factors for FPSOsanalysed.

Moatsos, 1. 2005

CHAPTER9

RELIABILITY

9.1 Introduction

The need to incorporate uncertainties in an engineering design has long been recognized

(Haldar & Mahadevan, 2000b). The absolute safety of a structure cannot be guaranteed as a

result of the unpredictability of future loading conditions; the inability to obtain and express

the in-place material properties accurately; the use of simplified assumptions in predicting

the behaviour of the structure due to the loading under consideration; the limitations in the

numerical methods used; and human factors (e.g. errors and omissions). However, the

probability of structural failure can be limited to a reasonable level. The sti8matn of

structural failure probability is an important task for an engineer. The area of structural

reliability has grown at a tremendous rate in the last decade as it was described in Chapter 3

in the literature review of this thesis and many methods have been proposed, considering the

type of the problem, the parameters involved, and the uncertainty associated with these

parameters Structural reliability can be classified into two types: element reliability and

system reliability. The term element reliability (component reliability) refers to the

probability of survival of an individual element of a structure corresponding to a

performance criterion. The term system reliability refers to the probability of survival of the

structural system as a whole.

The manner, by which engineering structures respond to the loading imposed on them,

depends on the type and magnitude of the applied load and the structural strength and

stiffness of the particular structure. As very accurately stated by Me1chers (2001), whether

the response is considered satisfactory depends on the requirements which must be satisfied.

These include safety of the structure against collapse, limitations on damage, or on

deflections or some other form of criteria. Each of these requirements may be termed a limit

state and the 'violation' or 'failure' of a limit state can then be defined as the attainment of

an undesirable condition for the structure. There are various types of limit states, as

described in Chapter 1 of this thesis (Table 1.1) and each of the codes, depending on the

type of the code, uses a different type of approach in defining this limit state. From

observation it is known that very few structures col1apse, or require major repairs, so that

Moatsos, I.2005

Chapter 9.Reliability 344

the violation of the most serious limits states is a relatively rare occurrence. When such a

violation of a limit state does occur, the consequences may be extreme.

The study of structural reliability is concerned, as again defined by Melchers (2001), with

the calculation and prediction of the probability of limit state violation for an engineered

structural system at any stage during its life. In particular, the study of structural safety is

concerned with the violation of the ultimate or safety limit states for the structure. The

probability of occurrence of an event such as a limit state violation is a numerical measure

of the chance of its occurrence. This measure either may be obtained from measurements of

the long-term frequency of occurrence of the event for generally similar structures, or may

be simply a subjective estimate of the numerical value. In practice, it is seldom possible to

observe for a sufficiently long period of time, and a combination of subjective estimates and

frequency observations for structural components and properties may be used to predict the

probability of limit state violation for the structure.

In probabilistic assessments any uncertainty concerning a variable is taken into account

explicitly. This is not the case in traditional ways of measuring safety, such as the 'factor of

safety' or 'load factor' approaches. These are 'deterministic' measures since the variables

describing the structure, its strength and the applied loads are assumed to take on known (if

conservative) values about which the assumption is made to be no uncertainty.

As mentioned in Chapter 1, during the introduction of this thesis, there are various 'levels'

at which safety (or more generally) limit state violation can be defined and summarised in

(Table 9.1):

l. Levell: At the lowest, and simplest, level we have Level 1 procedures

providing a workable design method in which appropriate safety margins are

provided usually on a structural element basis by specifying a number of partial

safety factors related to some defined characteristic values of the basic variables. In

the strength model these values will usually correspond with the 'nominal' values

specified in design codes. No explicit reliability calculations are undertaken and the

levels of risk in different structures are essentially unknown. Design methods

involving a number of PSFs are likely to be of much greater practical value than

Level 2 and Level 3 methods.

Moatsos, I. 2005


2. Level2: Level 2 methods use means and second moment properties of load

and strength distributions for components and structural assemblies in terms of a

'reliability' or 'safety index' ,8which corresponds to a notional probability of failure

or level or reliability for each failure mode or limit state during the life of the

structure. Appropriate partial safety factors may then be derived for particular design

situations. These safety checks made only at selected points on the failure boundary

(as defined by the appropriate limit state) rather than as a continuous process, as at

Level 3. These methods may be used for analysis or design. Unfortunately, the

essential features are conceptually less straightforward than Level 3 methods which

need make no attempt to find the region of basic variable or state-space which has

the highest probability of failure density. This is central to Level 2 methods and

provides the basis for calculating PFSs at Levell.

3. Level3: Level 3 methods are 'exact' probabilistic analysis methods for whole

structural systems involving the convolution integral. They are conceptually

straightforward but in practice difficult to formulate and solve. They cannot be

directly used in design, for example, for a specified reliability level. Level 3

methods are the only methods which can satisfactorily incorporate all modes of

failure when estimating the total reliability. Very clearly such approaches are not

suitable for normal design purposes but there is much scope for the use of Level 3

techniques for checking the validity and accuracy of the simplified Level 2 and

Level 1 methods by analysis of specific structures.

4. Characteristic values are usually given as functions or mean values, coefficients of

variation and distribution types. As indicated from Level 2 the PSFs may be

deducted from Level 2. Level 1 methods can be made identical to Level 2 methods if

the PSFs are continuous functions of the means and variances of the basic variables

and of the safety indices. Existing Level 1 methods replace this continuous function

by discrete values of the factors. In general PSFs, can be associated with each basic

variable but this is inconvenient and in practice are subsumed in cognate groups

such as 'load' and 'strength' related, 'consequences', 'modelling', 'systems' (or

redundancy) etc.

Moatsos, I. 2005


9.2 Basics of Structural Reliability Analysis

The basic structural reliability problem considers only one load effect S resisted by one

resistance R. Each is described by a known probability density function fs() and fR()

respectively. As noted, S may be obtained from the applied loading Q through a structural

analysis (either deterministic or without random components). It is important that Rand S

are expressed in the same units. For convenience, but without loss of generality, only the

safety of a structural element will be considered here and as usual, that structural element

will be considered to have failed if its resistance R is less than the stress resultant S acting

on it. The probability PI of failure of the structural element can be stated in any of the

following ways:

PI=P(R~S)

PI = P(R-S s 0)

PI =p(~ ~1)PI = P(lnR-lnS ~O)

PI =[G(R,S)~O]

(9.1a)

(9.1b)

(9.1c)

(9.1d)

(9.1e)

with GO defined as the 'limit state function' and the probability of failure is identical with

the probability of limit state violation. All of the (Eq. 9.1) set of equations can also be

written in terms of Rand Q for the structure as a whole.

Quite general (marginal) density functions js andfs for Rand S respectively can be seen in

(Fig. 9.1) along with the joint (bivariate) density function fRS(r,s). For any infinitesimal

element (Lir..::is) the latter represent the probability that R takes on a value between rand

r+Lir and S a value between sand s+L1s. as Lir and zls each approach zero. In (Fig. 9.1) any

of the (Eq, 9.1) set of equations are represented by the hatched failure domain D, so that the

failure probability becomes:

PI =P(R-S~O)= JJfRS(r,s)drdsD

(9.2)

When Rand S are independent:

Moatsos, I.2005


fRS (r, s) = fR (r )fs (s) (9.3)

which combined with (Eq, 9.2) give:

00 s~r

PI = P(R -S ~ 0)= J JfR{r)fs(s)drds (9.4)

We have to note here that for any random variable X, the cumulative distributions function

is given by:

..Fx{x)=P(X)~x= Jfx{y)dy (9.5)

provided that x>y, it follows that for the common, but special case when Rand S are

independent then (Eq. 9.4) can be written in the single integral form:

..PI =P(R-S ~O)= JFR(x)fs(x)dx (9.6)

This is known as a 'convolution integral'. As it can be seen in (Fig. 9.2) the integral

ca1culates the probability of R being less than or equal to x or the probability that the actual

resistance R of the member is less than some value x. We define this as a representation of

failure. The termfs(x) represent the probability that the load effect S acting on the member

has a value between x and x+Ax in the limit as Ax approaches zero. By considering all

possible values of x, i.e. by taking the integral over all x, the total failure probability is

obtained. This is also seen in (Fig. 9.3) where the (marginal) density functions js andfs have

been drawn along the same axis. Through integration of fRO in (Eq. 9.4), the order of

integration was reduced by one. This is convenient and useful but not always possible and

hence this cannot be generalised but in this case it was possible as R was assumed

independent of S. In general, dependence between variables should be considered. An

alternative to (Eq. 9.6) is:

Moatsos, I. 2005


DO

Pt = ~l-Fs(x)lrR(x}dx (9.7)

which is simply the total of the failure probabilities over all the cases of resistance for which

the load exceeds the resistance. The lower limit of integration shown in (Eq. 9.4) to (Eq.

9.7) may not be totally satisfactory, since the 'negative' resistance usually is not possible.

The lower integration limit therefore should be strictly zero, although this may be

inconvenient and slightly inaccurate if R & S are both modelled by distributions unlimited

in the lower tail, such as in the case of normal or Gaussian distributions. The inaccuracy

arises strictly from the modelling of Rand/or S and not from the theory involved with (Eq.

9.4) to (Eq. 9.7). This important point is sometimes overlooked in discussions about

appropriate distributions to represent random variables.

The fundamental variables which defined and characterize the behaviour and safety of a

structure may be termed as the basic variables. These are variables used in traditional

structural analysis and design such as dimensions, densities or unit weights, materials, loads

or material strengths. It is convenient to choose the basic variables such that they are

independent from one another but this may not always be the case. Dependence between

basic variables usually adds some complexity to reliability analysis and it is important that

the dependence structure between the variables be known and expressible in some form.

Usually this will be through a correlation matrix but this can at best provide only limited

information. The probability distributions to be assigned to the basic variables depend on

the knowledge that is available. If it can be assumed that past observations and experience

for similar structures can be used for the structure under consideration the probability

distributions might be inferred directly from such observed data. More generally, subjective

information may be employed or some combination of techniques is required as there are

seldom sufficient data available to identify only one distribution as appropriate. In a lot of

cases physical reasoning may be used to suggest an appropriate probability distribution and

where a basic variable consists of the sum of many other variables which are not explicitly

considered, the central limit theorem can be invoked to predict that normal distributions can

be used. It is not always possible to describe each basic variable by an appropriate

probability distribution as the required information may not be available and in this case a

'point estimate' of the value of the variables can be used as an estimate of its mean and its

Moatsos, I. 2005


variance. This is known as a 'second moment' representation and can be interpreted is that

in the absence of more precise data, the variable might be assumed to have a normal

distribution which is completely described by the mean and the variance, the first two

moments.

9.3 Uncertainties

Identification of uncertainties for complex systems can be a very difficult and time

consuming task and usually it is advantageous to use a systematic scheme to help to

enumerate all operational and environmental loading states and for each consider possible

combinations of error and malfunction. There are various ways in which the types of

uncertainties might be classified. One is to distinguish between 'aleatory' (or intrinsic)

uncertainty referring to underlying, inherent uncertainties and 'epistemic' uncertainty

referring to uncertainties which might be reduced with additional data or information, better

modelling and better parameter estimation. We can also classify uncertainties (DNV, 1992)

more in detail as:

1. Phenomenological uncertainties, resulting from an apparently 'unimaginable'

phenomenon occurring to cause structural failure and being of particular importance

for novel projects. Evidently, only subjective estimates of the effect of this type of

uncertainty can be given.

2. Decision uncertainties, arising In connection with the decision as to whether a

particular phenomenon has occurred. In terms of limit states it is concerned purely

with the decision as to whether a limit state violation has occurred.

3. Modelling uncertainties, associated with the use of one (or more) simplified

relationship between the basic variables to represent the 'real' relationship or

phenomenon of interest. In its simplest form it concerns the uncertainty In

representation of physical behaviour, such as through limit state equations.

Modelling uncertainty is often simply due to the lack of knowledge and it can easily

be reduced with research or increased availability of data.

4. Prediction uncertainties, associated with the refinement on knowledge available on

the variables and the system analysed, particularly during the construction phase as

actual data on the strength and loading replaces original estimates which was based

on past performance and experiences with similar systems.

Moatsos, I. 2005


5. Physical uncertainties, which is identified with the inherent random nature of a basic

variable. It usually cannot be eliminated but it can be reduced with greater

availability of data or in some cases with greater effort in quality control. Generally,

the physical uncertainty for any basic variable is not known a priori and must be

estimated from observations of the variable or be assessed subjectively.

6. Statistical uncertainties, caused by the observations of the variables not representing

it perfectly and resulting in bias in the data as recorded but also from different

statistical estimators produced from different sample data sets. Statistical uncertainty

can be incorporated in a reliability analysis by letting the parameters such as the

mean and the variance themselves be random variables. Alternative the reliability

analysis might be repeated using different values of the parameters to indicate

sensitivity.

7. Human factor uncertainties, resulting from human involvement in the design,

construction and use of systems. They can be considered as due to the effects of

human errors and human intervention and in practice there is interaction between the

two.

9.4 Time-Invariant Component Reliability

Reliability analysis methods were developed corresponding to limit state functions of

different type and complexity, as it can be seen in Ang & Tang (1975) & (1984), Madsen et

al. (1986), Melchers (2001) and Thoft-Christensen & Baker (1982) the first step toward

evaluating the reliability of a structure is to decide on the relevant load and resistance

parameters, called the basic variables Xi, and the functional relationship among them. This

can be described in mathematical terms as:

(9.8)

The failure surface or performance function of the limit stet of interest can then be defined

as Z=O. Using (Eq. 9.8), failure occurs when Z<O and therefore the probability of failure PI

is given by the integral:

(9.9)

Moatsos, I.2005


in which !x(Xj,X2, ••• ,Xn) is the joint probability density function for Xj,X2, ... ,Xn and the

integration is performed over the region in which gr. )<0. If the random variables are

statistically independent, then the joint probability density function may be replaced by the

product of the individual density functions in the integral. The computation of Pt by (Eq.

9.9) is called the full distributional approach and can be considered to the fundamental

equation of structural reliability analysis, In general the joint probability density function of

random variables is practically impossible to obtain. Even if this function is available, the

evaluation of the multiple integral is extremely complicated. Therefore, one possible

approach is to use analytical approximations of this integral that are simpler to compute. For

clarity of presentation, all these methods can be grouped into two types, namely, first- and

second-order reliability methods (FORM and SORM). The limit state functions of interest

can be linear or nonlinear functions of the basic variables. FORM can be used to evaluate

(Eq. 9.9) when the limit state function is a linear function of the uncorrelated normal

variables or when the nonlinear limit state function is represented by the first-order (linear)

approximation, that is, by a tangent at the design point. The SORM estimates the probability

of failure by approximating the nonlinear linear state function, including a linear limit state

function with correlated non-normal variables, by a second-order representation.

9.5 FORM & SORM Reliability Methods

9.5.1 Introduction

The development of FORM & SORM can be traced historically to second-moment

methods, which used the information on first and second moments of the random variables.

These are the first-order second-moment (FOSM) by Cornell (1969) and advanced first-

order second moment (AFOSM) methods (Ravindra et al., 1974) which dealt with the

problem of the variables not being statistically independent normal or lognormal distributed,

nor the performance function being a simple additive or multiplicative function of these

variables, as required by FOSM.

According to Cornell (1969), a limit state function is defined as:

Z=R-S (9.10)

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Assuming that Rand S are statistically independent normally distributed random variables,

the variable Z is also normally distributed and its mean and variance can be determined

from:

(9.11)

The event of failure is R<S, or Z<O and the probability of failure is given from:

(9.12)

where l/J is the cumulative distribution function for a standard normal variable. Thus the

probability of failure depends on the ratio of the mean value of Z to its standard deviation,

which Cornell (1969) named as safety index (reliability index) and denoted it as /3:

(9.13)

and hence (Eq. 9.12) can be re-written as:

P f = <1>(- /3) (9.14)

Nevertheless, FOSM also has serious drawbacks in its approach as it does not use the

distribution information about the variables even if they are available. More importantly

Cornell's safety index fails to be constant under different but 'mechanically equivalent'

formulations of the same performance function. More particularly they can be linked to the

Hasofer-Lind (1974) approach, which was developed to deal with the lack of invariance

noticed in all proposed approaches so far, and his definition of the reliability index as the

minimum distance of the limit state surface from the origin which can be extended to

estimate the probability of failure.

The Hasofer-Lind (1974) (H-L) method first defines the reduced variables as:

Moatsos, I. 2005


. X. -X. ( )X; = I I , i = 1,2,... ,n0';

(9.15)

where Xi' is a random variable with zero mean and unit standard deviation. Equation (Eq.

9.15) is used to transform the original limit state g(X)=O, to the reduced limit state, g(X';=O.

We define the X coordinate system as the original coordinate system, X· as the transformed

or reduced coordinate system and Y as the reduced, uncorrelated, standard normal

coordinate system. A safety index PHL is then defined as the minimum distance from the

origin of the axes in the reduced coordinate system, to the limit state surface (failure

surface):

(9.16)

The minimum distance point on the limit state surface is called the design point or checking

point, It is denoted by x· in the original space or x'· in the reduced variable space. In the

space of the reduced variables, the limit state equation can be represented as shown in (Fig.

9.4) with the safe and failure regions clearly marked. If we examine (Fig. 9.4) it is evident

that if the failure line (limit state line) is closer to the origin, the failure region is larger and

if it is farther away from the origin, the failure region is smaller. Thus the position of the

limit state surface relative to the origin is a measure of the reliability of the system. The

distance of the limit state line from the origin is:

(9.17)

which is essentially the reliability index defined by Cornell (1969) for normal variables R

and S. In general for many random variables represented by the vector X=(X/,X2, ... ,Xn), the

limit state g(X)=O is a nonlinear function as shown for two variables in (Fig. 9.5) and the

computation of the minimum distance becomes an optimisation problem:

Minimize D = .JX TX· subject to the constraint g(X) = 0 (9.18)

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for which an algorithm was formulated by Rackwitz (1976) to compute PilL and x,t. Thisalgorithm is shown geometrically in (Fig. 9.6). The algorithm constructs a linear

approximation to the limit state at every search point and finds the distance from the origin

to the linear limit state. This is a first order approach similar to the FOSM method with the

important difference that the limit state becomes linear at the most probable failure point

rather than the mean values of the random variables. Ditlevsen (1979) showed that for a

nonlinear limit state surface, PlfL lacks comparability and that the ordering of /3JIL values

may not be consistent with the ordering of actual reliabilities. An example of this can be

seen in (Fig. 9.7) with two limit states surfaces: one flat and the other curved. The shaded

region to the right of each limit state represents the corresponding failure region. The

structure with the flat limit state has higher reliability than the one with the curved limit

state surface but the PilL values are identical for both surfaces and suggest equal reliability.

As already mentioned the Hasofer-Lind definition of the reliability index as the minimum

distance of the limit state surface from the origin may be extended to estimate the

probability of failure. The information on the distributions of the random variables may also

be included in this computation. The probability of failure has been estimated using two

types of approximations to the limit state at the design point" first order (leading to the

name FORM) and second order (leading to the name SORM).

9.5.2 FORM

The Hasofer-Lind reliability index can be exactly related to the failure probability by using

(Eq. 9.14) if all the variables are normally distributed and the limit state surface is linear.

For the nonlinear limit state surface, the FORM uses a linear approximation to the limit

state at the design point, and estimates the probability of failure as PF l/J( -PilL), as illustrated

in (Fig. 9.7). If all the variables are not normally distributed, as is common in structural

problems, then it is difficult to relate PHL to the exact probability of failure. Rackwitz &

Fiessler (1976) suggested that this problem could be solved by transforming the nonnormal

variable in to equivalent normal variables and the FORM method was born.

Conceptually ths transformation can be made in several ways since a normal variable can be

described uniquely by two parameters (the mean and standard deviation) and any two

appropriate conditions can be used for this purpose. In the method the parameters of the

Moatsos, I.2005


normal distribution are estimated by imposing two conditions. The cumulative distributions

functions and the probability density functions of the actual variables and equivalent normal

variables should be equal at the checking point (x/,x/, ... ,xn"') on the failure surface. The

mean value and standard deviation of the equivalent normal variables are

(9.19)

(9.20)

in which F; and f are the non normal cumulative distribution and density functions of X, and

l/J and ¢are the cumulative distribution and density function of the standard normal variate.

Having determined (Eq. 9.19) and (Eq.(9.20) and proceeding similarly to the case in which

all random variables are normal, using the method of Langrage multipliers according to

Sinozuka (1983), the minimum distance to the design point is obtained as:

~n .*( ag ).L.,;i=t

Xj ax;PHL = - 2"

1::,(::;)(9.21)

where the derivatives are evaluated at (X/··,X2·"', ••• ,xn·"'). The asterisk after the derivative

indicates that is evaluated at the same interval. The design point is given by:

(9.23)

where:

(9.24)

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Are the cosines along the coordinate axes Xi'. In the space of the original variables, the

design point is given from:

(9.25)

Fot he calculation of (Eq, 9.25) & (Eq. 9.24) the same algorithm by Rackwitz (1976) as

described in (Section 9.5.1) can be used. The above system of equations (Eq. 9.21) to (Eq.

9.25) can be solved to obtain the value of ~HLand (Eq. 9.14) can be used to calculate the

probability of failure. The entire approach is often referred to as the Rackwitz-Fiessler

algorithm and has been extensively used in all relevant literature. Chen and Lind (1982)

proposed an extension of the Rackwitz-Fiessler algorithm by using a three parameter

approximation. The third parameter A is established, in addition to the mean and standard

deviation by imposing the condition that at the design point the slopes of the probability

density function be equal for both the original and the transformed, normal distributions. As

the additional parameter was introduced to control the transformation between the original

and equivalent normal distributions, it was anticipated that the Chen-Lind method would

produce more accurate estimates of the probability of failure but research has shown (Wu,

1984) that the two methods generally have the same estimates of the probability of failure

and in very limited cases the Chen-Lind method performs better that the Rackwitz-Fiessler

method. Both methods are sometimes referred to as advanced first-order second-moment

methods (AFOSM).

9.5.3 SO~1

The limit state could be nonlinear as a result of the nonlinear relationship between the

random variables and the limit state function, or as a result of some variables being

nonnormal. Even a linear limit state in the original space becomes nonlinear when

transformed to the standard normal space (which is where the search for the minimum

distance space is conducted) if any of the variables is nonnormal but also the transformation

from correlated to uncorrelated variables might induce nonlinearity. If the joint probability

density function of the random variables decays rapidly, as we move away from the

minimum distance point, then the above first-order estimate of the probability of failure is

quite accurate. If on the other hand the decay is slow and the limit state highly nonlinear,

then one must use a higher order approximation for the computation of the PI- Ditlevsen

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(1979a) suggested the use of a polyhedral envelope for the nonlinear limit state, as seen in

(Fig. 9.8) consisting of tangent hyperplanes at selected minimum distance points on the

limit state. The PI is then obtained through the union of the failure regions defined by the

individual hyperplanes providing a better estimate than a single approximation at the global

minimum distance point. The approach, sometimes referred to as a multiple-point FORM,

results in bounds on the failure probability resulting from the difficulty in computing the

joint probability of multiple failure regions. The following second-order bounds have been

derived by Ditlevsen (1979b):

(9.26)

where pt is the probability of the most probable failure region, Pi is the probability of the irh

failure regions and Pij is the joint probability of the irh andr failure regions.

An alternative to polyhedral surface is the construction of a second-order approximation ath

the minimum distance point. This type of computation is essentially referred to as second-

order reliability method (SORM), taking into account the curvature of the limit state around

the minimum distance point. Fiessler et al. (1979) explored the use of various quadratic

approximations and a closed-form solution for PI of a region bounded by a quadratic limit

was given by Breitung (1984), using asymptotic approximations as:

n-I 1

Pf == <1>(- P)TI (1+ {lk; t2;=1

(9.27)

where k, denotes the ;rh main curvature of the limit state at the minimum distance point.

According to this approach this second-order probability estimate asymptotically

approaches the first-order estimate as P approaches infinity, if {lki remains constant. Tvedt

(1983) & (1990) proposed three formulas to include curvatures in the probability estimate

which become clear when we consider a rotated standard normal space r' in which the y'n

axis coincides with the perpendicular from the origin to the tangent hyperplane at the

minimum distance point y. (Der Kiureghian et al., 1987). This is achieved by an orthogonal

transformation:

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y'=RY (9.28)

where the nth row of R is selected to be y*/(y*Ty*)l!2. A standard Gram-Schmidt algorithm

may be used to determine R. Consider a second-order surface in this rotated standard space

as:

(9.29)

where A is the (n-l)x(n-l) second derivative matrix. The elements of A are obtained from:

(RDRTt ( )aij = IVG(l ~' i, j = 1,2,... ,n-1 (9.30)

where D is the nxn second derivative matrix of the limit state surface in the standard normal

space evaluated at the design point, R is the rotation matrix and VG(Y·) is the gradient

vector in the standard space. It is also interesting to not that the main curvatures ki, used in

Breitung's formula previously mentioned are eigenvalues of the matrix A. With these

definitions, Tvedt's three term (TT) formula is:

where I is the identity matrix, ¢ is the standard normal density function, and i=(-l )112. The

first term is equivalent to the result of Breitung's formula, but is expressed in determinant

form. Tvedt's single-integral formula is:

Moatsos, I.2005


where the summation represents a k-point Gauss-Laguerre quadrature approximation with

weights Wj and abscissas Sj. Tvedt's double-integral formula is:

(9.33)

1

X (;32 +2S)2 exp(- s - u 2}tsdu

where rp(.) denotes the root with positive real part. For a quadratic safe set, this expression

is exact where the main curvatures ki are positive. In other cases, it provides a better

approximation to the probability than the previous two formulas. Der Kiureghian et al.

(1987) obtained a quadratic approximation by fitting the limit state at (2n-n) discrete points

in the design point neighbourhood in the rotated space mentioned. The principal directions

of the approximating paraboloid are selected to coincide with the coordinate axes of the

rotated space. The approximating paraboloid then becomes:

1 n-l, ,,'2YII =P+ 2~aiYi (9.34)

where a, are the principal curvatures. Now considering the two-dimensional space of Yi' and

y'n. as shown in (Fig. 9.9). Two semi-parabolas are first defined that are tangent to the limit

state at the design point and pass through the two fitting points with coordinates(±kp,77±i)'

The approximating paraboloid is a weighted average of the two semi-parabolas. The

principal curvatures a, used in the approximating paraboloid are determined by requiring

that the probability content on the unsafe side be equal to the sum of the probability content

defined by the two semi-parabolas. Using Breitung's approximation, this can be expressed

as:

(9.35)

where:

Moatsos, I. 2005


(9.36)

are the curvatures of the two semi-parabolas. As the principal directions of this point-fitted

paraboloid are assumed to coincide with the coordinate aces in the rotated space, the effect

of second-order cross-derivative forms is ignored and hence less computational effort is

required. For a problem with n variables, at most four deterministic runs per fitting point are

required with a total of 8(n-l) computations to define the paraboloid completely. On the

other hand, the formulas of Breitung and Tvedt imply curvature-fitted paraboloids, and

require and complete second-order deri vati ve matrix, requiring a total of 2(n-l/

computations using a central difference scheme, and n(n+l)l2 computations using a

forwards difference scheme. This difference in the amount of computation becomes

significant for problems with large numbers of random variables and should not really be an

issue during this study but nevertheless it should be noted for use but future readers of this

study.

It should also be emphasised that all methods mentioned so far, the original variables

(which can in some cases be correlated and nonnormal) are transformed to an equivalent

uncorrelated standard normal space to search for the minimum distance point on the limit

state surface. It is not necessary to make such a transformation as Breitung (1989)

developed a procedure that maximizes the 'loglikelihood' function of the probability

distribution in the original space. Second-order approximations to the limit state surface are

then constructed at these maximum likelihood points.

9.6 Time Dependent Reliability

In general, the loads which are applied to a structure fluctuate with time and are of uncertain

value at any point in time. This is carried over directly to the load effects (or internal

actions) S. In a similar fashion the structural resistance R will be a function of time (but not

fluctuating) as a result of deterioration and similar actions. Loads have a tendency to

increase, and resistances to decrease, with time and in most cases uncertainty in both

quantities increases with times. Hence the probability density functions is( ) and iR( )

become wider and flatter with time and the mean values of Sand R also change with time.

Moatsos, I. 2005


The general reliability problem can be seen illustrated in (Fig. 9.10). The safety limit state

will be violated whenever, at any time t:

R{t}- S{t}< 0 or ~~:~< I (9.37)

The probability of this occurring for anyone load application (or load cycle) is the

probability of limit state violation, or simply the probability of failure PI' Roughly it may be

represented by the amount of overlap of the probability density functions fR and fs in (Fig.

9.10). Since this overlap may vary with time, PI also may be a function of time but in many

situations it is convenient to assume that neither Q nor S is a function of time as in the case

of the load Q being applied once only to the structure and the probability of limit state

violation is sought for that load application only. However, if the load is applied for a large

number of times and R is taken as constant, then it is the maximum value of that load within

a given time interval [0, TJ which is of interest. It can then be assumed that the structure can

fail under the once only application of this maximum load. In this case the load is more

properly presented by an extreme value distribution (Me1chers, 2001) such as the Gumbel

(EV-I) or the Frechet (EV-II). If this is done, the effect of time may now be ignored in the

reliability calculations but this approach is not satisfactory when more than one load is

involved or when the resistance changes with time.

The elementary reliability problem as stated in (Eq. 9.1) in 'stochastic' or 'time-variant'

terms with a resistance R(t) and a load effect Set), at time t becomes:

P f (t) = P[R{t) ~ S{t)] (9.38)

If the instantaneous probability density functions jijr) and fit) of R(t) and Set) respectively

are known, the instantaneous failure probability pjt) can be obtained from the convolution

integral (Eq. 9.6). Schematically, the changes in fRet), fit) and pjt) with time can be

depicted in (Fig. 9.10).

Now (Eq. 9.38) only has meaning if the load effect Set) increases in value at time t

(otherwise failure could have occurred earlier) or if the random load effect is re-applied

Moatsos, I.2005


precisely at this time. Failure could not occur precisely at the very instant of time t

(assuming of course that at time less than t the member was safe). We can conclude hence

that a change in load or load effect is required if:

1. There are discrete load changes

2. For continuous time-varying loads, an arbitrary small increment (i, in time, is

considered instead of an instantaneous time t.

As a result of this we can hence formulate:

p/t)= ffx(,) [X (t)]dx (t)G[X(I)~O

(9.39)

which in two-dimensional space may be represented according to (Fig. 9.1) for any given

time t. As mentioned already X(t) is a vector of the basic variables. In principle though, the

instantaneous failure probability, as formulated in (Eq. 9.38) and (Eq. 9.39) can be

integrated over an interval of time [O,tJ to obtain the failure probability over that period. In

practice however, the instantaneous value of pit) usually is correlated to the value

p f (t + (i), (i ~ 0, since typically the processes X(t) themselves are correlated in time. This

can be easily identified in a typical 'sample' function or 'realization' of a random process

load effect, as illustrated in (Fig. 9.11).

The classical approach according to MeIchers (2001) is to consider the integration

transformed to the load or load effect process, which is often assumed to be represented,

over the total time period, by an extreme value distribution. The resistance is assumed

essentially time invariant. This approach is (often referred to as 'classical' reliability) forms

the basis of this study. A refinement is to consider shorter periods of time, such as in the

duration of a storm or a year, and to apply extreme value theory within that period. Simple

ideas similar to the concept of the return period then can be used to determine the failure

probability over the lifetime of the structure. Such type of analysis is often preferred for

practical reliability analysis of structures such as offshore platforms subject to definable and

discrete loading events.

Moatsos, I.2005


A somewhat different approach to the problem is to consider the safety margin associated

with (Eq. 9.38) as:

z{t) = R{t)- S{t) (9.40)

and to establish the probability that Z(t) becomes zero or less in the lifetime tt. of the

structure. This constitutes a so-called 'crossing' problem. The time at which Z(t) becomes

less than zero for the first time is called the 'time to failure' (Fig. 9.12) and is a random

variable. The probability that Z{t):::;;0 occurs during tt. is called the 'first-passage'

probability. The corresponding situation in two-variable space is illustrated in (Fig. 9.13).

The probability that the vector process X(t) will leave the safe region G(x»D (the

probability that an 'out-crossing' will occur) during the structural lifetime tt. is again in the

so called 'first-passage' probability. This is equal to the probability of failure of the

structure since failure is defined by G{X):::;; O. The first passage concept is more general that

the classical approaches as there is no restriction on the form of G(X). However, the

determination of the first passage probability and a proper understanding of the concept of

stochastic processes as described in (Chapter 8). For the basic reliability problem to be

applicable in the cases of more than one load or load effect it is necessary to combine two or

more load effects into an equivalent load effect as it is extensively described in (Chapter 8).

9.7 Time-Variant Component Reliability

Time-variant reliability is more difficult to compute that time-invariant component

reliability. In this case one is not interested in the time dependent failure probability

function Pjt) where t is treated as a parameter but in quantities like the probability of first

passage into the failure domain, the total duration of individual exceedances and other

related criteria. The quantity

N(t) = fix (x,t)d.xg(X.l )so

(9.41)

is rather denoted by non-availability so that,

A(t)= 1-N(t) (9.42)

Moatsos, I. 2005


is the availability. Both quantities can be easily determined.

For the determination of Time-Variant Component Reliability of the TankerIFPSO

structures analysed in this Thesis, STRUREL(RCP, 1999) software was used, developed by

RCP Reliability Consulting, Munich Germany and specifically its COMREL- TV Version

7.0 component. COMREL-TI can only handle criteria of the first mentioned type. In

principle the basic formulation then is

(9.43)

where T is the random time of exit into the failure domain and [0, tl is the considered time

interval. If the component does not fail at time t=0 failure occurs at a random time and the

distribution function of T must be known. Unfortunately this is rarely the case. Exceptions

are the failure times of non-structural components (electrical or other) where often rich

statistical material is available. Then it is also possible to use a time-invariant approach

because the limit state will simply be:

g{x}= T -1< 0 (9.44)

In all other cases T, must be inferred from the characteristics of the random process

affecting the performance of the component. T must be considered as a first passage time,

i.e. is the time where the component enters the failure domain for the first time given that

the component was in the safe state at time 1=0. Exact first passage time distributions are

known for only very few types of processes which generally are of little practical interest.

In COMREL-TV the so called out crossing approach is implemented for the determination

of the probability of first passage failure. As in time-invariant component reliability there

exists a state function depending on random vectors and on random process variables. More

specifically, COMREL-TV distinguishes between three types of variables:

• R is a vector of random variables as in time-invariant reliability. Its distribution

parameters can be deterministic functions of time. This vector is used to model

Moatsos, I.2005


resistance variables. The most important characteristics of this type of variable is

that they are non-ergodic.

• Q is a vector of stationary or ergodic sequences. Usually, it is used to model long-

term variations in time (traffic, sea states, wind velocity regimes, etc.). Quite in

general these variables determine the fluctuating parameters of the random process

variables described next.

• S is a vector of (sufficient mixing) not necessarily stationary random process

variables whose parameters can depend on Q and/or R. The vector S is further

subdivided into:

o A vector J of rectangular wave renewal processes

o A vector D of differentiable processes (Gaussian and non-Gaussian)

The safe state, limit state and failure state of the component is defined for:

g(r,q,s(t ),t) > 0g(r,q,s(t ),t) = 0g(r,q,s(t ),t) ~ 0

(9.45)

and the state function can contain time as a parameter too.

A rate of out-crossings into the failure domain conditional on q and r can be defined:

v+ (F, 1'1 r.q )lim4~o.!_ p({g(S(1'), 1'1 r,q) > O}(l{g(S(1' +~),1'+ ~ I r,q) s o})~

. (9.46)

F denotes the failure domain {g(s(t),tI r,q)~O}. In order to exist it is necessary that the

limiting operation can be performed. This excludes certain processes which fluctuate too

rapidly in time. Further in small time interval there is at most one crossing. The probability

of more than one crossing is negligible small. Then the process of crossings is cal1ed a

regular point process.

The mean number of crossings in the time interval [tj, t21 conditional on q and r can be

determined from,

Moatsos, I. 2005


'2E[N+(tpt2)1 q,r]= JV+(F,rl q,r)dr (9.47)

Thus, the time-dependent out-crossing rates are additive for a regular process. Then, it has

been shown by Bolotin (1981) that an upper bound to the conditional probability is:

(9.48)

If further the process is strongly mixing it is asymptotically for Pt (t1 ,t21 q, r) ~ 0 according

to Cramer and Leadbetter (1967):

(9.49)

The conditions can be removed by integration. Whereas the expectation operation with

respect to the condition on q can be performed inside the exponent by making use of the

ergodic property of Q, it cannot be done with respect to the R-variables.

(9.50)

Schall et al. (1991) showed that for the upper bound solution

(9.51)

A lower bound is also available but is not particularly of interest in this study and the

detailed formulation can be found in (RCP, 1999).

COMREL-TV offers for the general case upper bound solution together with a, not always

close, lower bound solution. In most cases PI.!l) is negligible small. It will always be

calculated if the upper bound solution is chosen. For two special cases the expectation with

respect to R in the asymptotic approximation can also be performed by simple importance

sampling Monte Carlo integration. For the upper bound solution R-variables are treated like

Q-variables and for all computations a probability distribution transformation into standard

Moatsos, I.2005


space, as in time-invariant reliability is performed. Unfortunately as it can be seen from

Engelund et al. (1995) the out-crossing approach cannot be improved easily.

For all computations a probability distribution transformation into standard space as in time-

invariant reliability is performed. It is also assumed that random processes start with

random initial conditions throughout. Since it has been found that asymptotic solutions also

with respect to the time integration (RCP, 1999) are too inaccurate under non-asymptotic

conditions and pure first-order solutions are rarely satisfying, a compromise between

asymptotic solutions and somewhat more exact time integration schemes in implemented in

COMREL-TV. In all cases it is assured that the solutions implemented converge to

asymptotic solutions under appropriate conditions and the stationary or non-stationary

solution for linear failure surfaces (int the standard space) is always recovered. FORM

options, although generally available, are not recommended and the computational effort is

significantly larger than for time-invariant reliability problems, especially when general

intermittent processes are to be considered. The methods described above are of limited use

for dynamic systems. Then, it is not only difficult to assess the auto- and cross-correlation

structure of the interesting output quantities. Also, the combination of rectangular waves as

well as intermittencies as described above make little sense if passed through a dynamic

structure. The transient phases of the system generally lead to an oscillatory behaviour of

system states. Therefore, the time integration schemes with respect to time require a certain

amount of modifications.

9.8 Monte Carlo Simulation

9.8.1 Introduction

There are essentially three ways in which multidimensional integration can be performed

for structural reliability purposes:

1. Direct Integration (possible only in a very limited number of special cases).

2. Numerical Integration (Monet Carlo techniques).

3. Obviating the integration through transforming the integrand to a multi-normal joint

probability density function for which some special results are immediately

available (techniques which fall beyond the purposes of this study).

Moatsos, I. 2005


In practice, limit state functions usually are of more general form than linear functions and

random variables associated with these limit state functions are unlikely all to be normally

distributed random variables. Methods have developed to deal with these issues and

integration methods would be suitable, in principle. However, because of the rapidly

increasing computational demands as the number of dimensions increases (the so-caIled

"curse of dimensionality"), numerical integration of the classic variety has not found great

favour in reliability computations. Instead, researchers in the field have opted for methods

developed for other large integrations problems (Kahn, 1956) and described in standards

texts (Stroud, 1971) dealing with numerical integration. These methods are the simulation

or Monte Carlo Methods and they form a class of approximate numerical solutions to the

probability integral:

PI = p[G(X)~O]= J... JfJx}dxG(Xf-;O

(9.52)

applicable to problems for which the limit state function G(x)=O may have any form, and

for which the probabilistic description of the random variables Xi is unrestricted.

As the name implies, Monte Carlo Simulation techniques involve sampling at random to

simulate artificially a large number of experiments and to observe the result. In the case of

analysis for structural reliability, this means, in the simplest approach, sampling each

random variable Xi, randomly to give a sampling value Xi. The limit state function

G(x) = 0 is then checked. If the limit state is violated, the structure or structural element has

failed. The experiment is repeated many times, each time with a randomly chosen vector of

values. If N trials are conducted, the probability of failure is given approximately by:

(9.53)

where n(G(x;) ~ 0) denotes the number of trials n for which (G(x;) ~ 0). Obviously the

number N of trials required is related to the desired accuracy of Pt·

Moatsos, I. 2005


It is clear that in the Monte Carlo method a game of chance is constructed from known

probabilistic properties in order to solve the problem many times over, and from that to

deduce the required result, which in our case is the failure probability. In principle, Monte

Carlo Methods are only worth exploiting when the number of trials or simulations is less

than the number of integration points required in numerical integration. This is achieved for

higher dimensions by replacing the systematic selection of points by random selection,

under the assumption that the points so selected will be some way unbiased in their

representation of the function being integrated.

To apply Monte Carlo techniques to structural reliability problems it is necessary:

1. To develop systematic methods for numerical sampling of the basic variables X.

2. To select an appropriate economical and reliable simulation technique or sampling

strategy.

3. To consider the effect of the complexity of calculating G(x;) and the number of

basic variables on the simulation technique used.

4. For a given simulation technique to be able to determine the amount of sampling

required to obtain a reasonable estimate of PI'

Itmay be necessary also to deal with dependence between all or some of the basic variables.

9.8.2 Random Variate Generation

Basic variables only seldom have a uniform distribution. A sample value for a basic variable

with a given (non-uniform) distribution is called a random variate and can be obtained by a

number of mathematical techniques. The most general of these is the inverse transform

method. If we consider the basic variable Xi for which the cumulative distribution function-

Fx;(xj) must, by definition, lie in the range (0,1) as it can be seen in (Fig. 9.14).

The inverse transform technique is to generate a uniformly distributed random number

Ii(O ~ Ii ~ 1) and equate this to as Fx;(xj):

(9.54)

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This uniquely fixes the sample value Xi = Xi' provided that an analytic expression for the

inverse F:r~1 (r;) exists (as it does for the Weibull, Exponential, Gumbell and rectangularI

distributions among others). In these cases the inverse transform method is likely to be the

most efficient technique. The technique can also be applied to basic variables whose

cumulative distribution function has been obtained from direct observation.

9.8.3 Direct Sampling - Crude Monte Carlo

The technique as described in Section (9.6.1) is the simplest Monte Carlo approach for

reliability problem but certainly not the most efficient. The basis for its application is lies in

the traditional probability of limit state violation and may be expressed as:

(9.55)

where If J is an indicator function which equals 1 if f J is true and 0 if f J is false. Thus the

indicator function identifies the integration domain. If X j represents the jth vector of

random observations fromfx( ), it follows directly from sample statistics that

(9.56)

is an unbiased estimator of 1. Thus the expression in (Eq, 9.56) can provide a direct estimate

of Pt. In exploiting this procedure, three maters are of interest:

1. How to extract most information from the simulation points.

2. How many simulation points are needed for a given accuracy.

3. How to improve the sampling technique to obtain greater accuracy.

Let us consider all of these so as to have a complete view of how we can utilise this

technique most efficiently. It would be important to note that one way that the results of the

mentioned sampling technique may be represented is as a cumulative distribution function

Fa(g) as it can be see in (Fig. 9.15):

Moatsos, 1. 2005


Obviously, much of the range of Fc(g) is of little interest, since the structure or member is

(usually) amply safe. To estimate the failure probability the region for which G( ):::;;0,

which represents failure is clearly of most interest.

The estimation of Pf using (Eq. 9.56) can be improved by fitting an appropriate distribution

function through the points which G( ):::;;0, i.e. the left hand tail in (Fig. 9.15). However,

the choice of an appropriate distribution function may be difficult. Distributions which

could be of use for this purpose are the Johnson and Pearson distribution systems (Elderton

& Johnson, 1969). However it is possible that the parameters of the distribution function are

rather sensitive to extreme results in the region G( ):::;;O. In that case the choice of

distribution function parameters may not stabilize until N is quite large (Moses & Kinser,

1967). Rather than fitting a single distribution to the sample points, it is possible to fit a

sequence of distributions and to optimize their parameters to give a best-fit to the sample

points (Grigoriu, 1983).

9.8.4 Number of Samples Required

An estimate of the number of simulations required for a given confidence level may be

made as follows. Since G(X) is a random variable in X, the indicator function I[G(X):::;; 0] is

also a random variable, albeit with only two possible outcomes. It follows from the central

limit theorem that the distribution of 1] given by the sum of independent sample function

(Eq. 9.56) approaches a normal distribution as N ~ 00. The mean of this distribution is:

N

E(1I)= LE[/(G:::;;O)]=E[/(G:::;;O)];=1

(9.57)

which is equal to J, while the variance is given by:

N 1 a2

a;i =L -2 var[/( G s0)]= /(GSO)

;=1 N N(9.58)

which shows that the standard deviation of 1] and hence of the Monte Carlo estimate varies

directly with the standard deviation of I( ) and inversely with NI12• These observations are

Moatsos, 1. 2005


important in determining the number of simulations required for a particular level of

confidence. To actually calculate confidence levels, an estimate of ~ ( ) is required. The

variance is given:

(9.59)

so that the sample variance is given by:

(9.60)

where the last { } term is simply the mean (Eq. 9.60) or, by (Eq. 9.59) the estimate J: of PI'

On the basis that the central limit theorem applies, the following confidence statement can

be given for the number (h) of trails in which failure occurs:

p(- ka < 11 - J.l < +keY) = C (9.61)

where J.l is the expected value of 11 given by (Eq. 9.60) and eris given by (Eq. 9.58).

9.9 The Limit State Equation & Stochastic Model

As described in Section (9.2) of this chapter, according to the basic concept of the structural

theory of reliability analysis, the first step toward evaluating the reliability of a structure is

to decide on the relevant load and resistance parameters, cal1ed the basic variables Xi, and

the functional relationship among them. This can be described in mathematical terms as:

(9.62)

The failure surface or performance function of the limit stet of interest can then be defined

as Z=O. This is the boundary between the safe and unsafe regions in the design parameter

space, and it also represents a state beyond which a structure can no longer fulfil the

function for which it was designed. The limit state equation (performance function) plays an

important role in the development of structural reliability analysis methods. A limit state

Moatsos, I. 2005


function can be an implicit or explicit function of basic random variables and it can be in a

simple or complicated form.

In limit state analysis the classic treatment of the problem considers the hull to be a box

beam experiencing pure bending. The problem is then just a simple beam in bending and

can be written as:

(9.63)

where Mu is the ultimate bending moment, Z is the sections modulus of the vessel at the

section of interest, and O'y is the tensile yield stress of the vessel material. The limit state for

hull girder bending can be expressed as already mentioned by:

G=R-L (9.64)

where G is the performance function, R is the resistance and L is the load. When G:::;;0 the

structure fails; when G>O the structure survives. When expressed in terms of (Eq. 9.63) a

nonlinear performance function is the result. This form separates the load into wave and

still-water bending moments, Mw and Msw, respectively; and G is expressed in units of the

bending moments:

(9.65)

Here the product O'yZ represents the resistance strength of the system. The still-water

bending moment Msw could be considered as one load effect and the wave-induced bending

moment Mw as another load effect. Each will have its own distributions type, mean vale and

coefficient of variation. Each will represent the distribution of the loading in the lifetime of

the vessel. Although this is not a very sophisticated manner of combining load effects, it is

useful to show the flexibility of simulation methods.

As described in (Section 9.3) of this Chapter when describing the nature of uncertainties, in

reliability analyses, all design variables are in principle regarded as random variables with

certain level of uncertainties. The probabilistic characteristics of the random variables can

Moatsos, I. 2005


be quantified by regression analysis based on statistical observations. In addition to mean

and standard deviation of the variables, the type of the probability distribution has a crucial

impact in reliability analysis, since the predicted reliability significantly depends on its tail

shape. When detailed information for the particular random variable is not available, a

relevant type of the probability distribution may be presumed. Normal or log-normal

distribution is typically adopted for analysis of ship structural reliability (Paik & Frieze,

200 1), the former being relevant for strength variables, while the latter is required for load

variables or the variables which always take positive values.

As stated in Chapter 8, traditionally, the total bending moment M, is defined as the extreme

algebraic sum of still water moment Msw and wave-induced moment Mw, as follows:

(9.66)

When we adopt this approach for calculation of the total bending moment, the failure

condition associated with hull girder collapse can be written as:

(9.67)

where Mu is the random variable representing the hull girder ultimate strength, Msw and Mw

are random variables representing the still water or wave induced bending moments, Xu the

random variable representing the model uncertainties associated with hull girder ultimate

strength determination. and Xsw, Xw the random variables representing the model

uncertainties associated with still water or wave-induced bending moment predictions. The

failure conditions (Eq, 9.67) portrays the limit state function for hull girder collapse as

function of six variables. However Mu involves parameters related to geometric and material

properties (plate thickness, yield strength, Young's modulus) of the various structural

members in a functional form. The value of member thickness at any particular time will be

a function of time-variant structural degradation due to corrosion or fatigue when the safety

and reliability of aging structures is considered. Also the wave-induced bending moment

involves random parameters related to sea states, such as the wave height, and operational

condition, such as the ship speed and heading. Therefore, the number of random variables

considered in the limit state function is normally significantly more than in (Eq. 9.67).

Moatsos, I. 2005


The mean still water bending moment Msw is normally calculated by substituting the mean

values of ship principal particulars into the design formula provided by a Classification

Society. The Msw so obtained is actually an extreme design value, and its use as a mean

value is usually pessimistic. The long-term variability in still water will depend on the ship

type, loading condition, voyage routes, changes in cargo loading patterns from voyage to

voyage, etc. The coefficient of variation (COV) associated with still water bending moment

us normally large and can be as high as 40% (Mansour & Hovem, 1994) and is usually

assumed to follow the normal distribution. To the extent that the mean of this distribution is

taken to coincide with the design still water bending moment value adopting a 40% COY

would be quite pessimistic. In a short-term analysis of the wave-induced bending moment

the inherent COY of the extreme can be shown to be approximately 10% (Paik & Frieze,

2(01). The mean value of the ultimate strength of the hull is calculated assuming that the

average value of the yield strength of the material is the Classification Society rule

minimum value, which can be pessimistic by perhaps 15%. For mean values of the plate

(initial) thickness and modulus of elasticity of the material, conventional nominal values can

be used. Other details of the statistical characterization of the inherent uncertainties

associated with plate thickness, yield strength and Young's modulus can be taken as

indicated in (Table 9.2) as indicated in (Mansour & Hovem, 1994). The time variant

strength can be considered to be normally distributed with a COY of 10%. Within the

context of the reliability analysis procedures used, such a simplified approach to the COY of

the ultimate strength is actually not necessary because the probability of failure could have

been calculated by direct input of the applicable means, and COY s associated with

geometric and material properties. It is often assumed that the probability density function

of any random variable representing a model uncertainty follows the normal distribution.

Typical means and COVs for model uncertainties used for such calculation can be founding

(Table 9.3) according to Mansour & Hovem (1994). It would be worth noting in this case

that the uncertainties listed in (Table 9.3) are actually estimated guesses and whenever

better information is available (Frieze & Plane, 1987) it is possible to refine such values.

Mansour & Hovem (1994) evaluated the reliability of ship hull girder strength with the

variation in the correlation coefficient between the still water and the wave-induced

components and they concluded that the interaction of these two load components might be

Moatsos, I.2005


usually ignored. The two loading components were considered independent and Ferry

Borges-Castanheta load combination method was applied to obtain a load combination

factor. The failure surface for the ultimate longitudinal strength of the hull girder was

defined as;

g(X) = Xu Mu - Mse - V'W Xnl Xw Mwe = 0 (9.66)

Mu, represents the ultimate bending moment capacity of the hull girders and a factor Xu,

(uncertainty on ultimate strength) is introduced in the failure surface equation in order to

account for the uncertainties in the ultimate strength model and in the material properties.

Teixeira (1997) estimated a realistic COV for the total uncertainty on ultimate strength to be

10%, which is in good agreement with Faulkner (1992) who proposed a COV of 10-15% for

the modelling uncertainty for flat panel collapse. Thus, Xu was assumed normally

distributed, with a mean value of 1.0 and a standard deviation of 0.10. The most probable

extreme still water bending moment, Mse, is calculated based on a mean still water moment

Msw. The still water bending moment is always hogging for this vessel. A COY of 15 %

was applied to this mean value. The load combination factor, 'lW, is introduced to account

for the low probability that the extreme still water and wave bending moments will occur at

the same instant. A factor of 0.78 for the structure analysed was obtained respectively, using

Ferry Borges-Castanheta load combination method as described in Chapter 8.

In addition to the non-linear effects, there are other uncertainties associated with the linear

strip theory programs. Different programs will use different procedures for calculating the

hydrodynamic coefficients. Dogliani et al. (1998) showed that the linear strip theory

programs generally over-predicted the wave induced bending moments at the 10-8

probability level. Shellin et al. (1996) identified large variations in long-term distributions

of midship induced loads based on transfer functions obtained by different methods. Values

of 10% for Xw (Uncertainty in wave load prediction) and 1.2 in Sagging and 0.8 in Hogging

for Xnl (Non-linear effects) were based on the previous research works carried out at

Glasgow University (Das, 1998) & (Maerli et al. 2000). Extreme vertical wave bending

moment, Mwe, was obtained by combining the short-term responses with the wave statistics

for the Fair Isle area as described in the procedure in Chapter 8. The long-term probability

Moatsos, L 2005


of exceedance of different wave-induced vertical bending moments was obtained, and a

Weibull distribution was fitted to the resulting distribution.

9.10 Time Invariant Reliability Results

Reliability analysis using a First Order Reliability Method (FORM) and a Second Order

Reliability Method (SORM) was performed on the structure by assuming that the ultimate

strength of the hull girder follows a Lognormal distribution with a coefficient of variation

(COV) of 10%, the wave bending moment following a Gumbel distribution with a COV of

15% and the still water bending moment a Gumbel distribution with a COV of 15%.

Although wave bending moment variations could often be in the range of 25% the 15%

figure was chosen as an initial starting point for the procedure. Reliability indices fl for the

structure in the range of temperatures examined and probabilities of failure Pt were obtained

for sagging and hogging conditions. As it can be seen in the Appendix of this Chapter (Fig.

9.16) depicts the temperature and corrosion effects in Pt in sagging condition for one of the

FPSOs analysed, and (Fig. 9.17) the similar effects on the reliability index fl.For hogging in

a similar fashion (Fig. 9.18) shows the effects in PI and (Fig. 9.19) in fl and the results

showed an obvious decrease in fl and an increase in the probability of failure as diurnal

change in temperature increased. The stochastic model used is in accordance to the

approaches used and described in Section (9.7) and can be found summarised in a tabular

form in (Table 9.4) and the limit state equation takes the form:

M" ~ Ultimate Bending Moment Capacity

A" ~ Uncertainty on Ultim.Strength

M S~ ~ Still Water Bending Moment

rp(J) ~ Load Combinat. Factor

A{J) ~ Uncertainty in Wave Load prediction

AnD} ~ Non -linear effectsM we ~ Extreme Vertical Wave Bending Moment

(9.67)

Results also show that fl values reduce following a 3rd order Polynomial trend whereas PI

values reduce following and exponential trend. In both cases the effect of temperature and

Moatsos, I. 2005


corrosion on the values is quite significant. Partial safety factors for the variables used in

reliability analysis could be obtained which would provide a code format for design

purposes and allow the design to be even further optimized. If a simple code format such as

¢R> YsMs +YwMw (9.68)

was assumed where (jJ, 'r.> and Yw are the partial safety factors for the strength R, the still

water bending moment Ms and Mw the wave bending moment respectively then the design

could be easily optimized. Partial safety factors shown in (Fig. 9.20) for sagging and (Fig.

9.21) for hogging, for all the variables influencing the probability of failure in the limit

state equation and for the determination of safety criteria for the structure, are obtained and

showed not to be affected by temperature changes in both sagging and hogging conditions

whereas in sagging the wave bending moment partial safety factor decreased as diurnal

temperature change increased as a result of the sign convention used that made only the

wave bending moment to have a negative effect on the limit state function.

9.11 Time Variant Reliability Results

The limit state function used and the stochastic model and the limit state function used for

the calculation of the instantaneous and time dependent through life reliability of the vessel

can be seen in (Eq. 9.69) and (Table 9.4).

(9.69)

, where MuCt) the ultimate strength as a function of the time dependent corrosion, MsCt) and

M....(t) the long term most probable values of the SWBM and VWBM, 'lfw the load

combination factor for SWBM and VWBM, Aw an uncertainty for non-linearity in the

prediction of the VWBM and Xu, xs, Xw the model uncertainties for predicting the hull girder

strength, SWBM and VWBM. Typical values for the random variables of model

uncertainties were used according to published research.

The instantaneous long term reliability of the vessel was obtained using the limit state

equation described in (Eq, 9.69) using a Second Order Reliability Method (SORM)

Moatsos, I.2005


approach but without taking into account of time and computing the probabilities of failure

and reliability indices by using the values that result as most probable extremes for the loads

and for each corrosion year for the ultimate strength and that are distributed according to the

stochastic model.

For the time-variant reliability results, the variance of the variables with time was taken into

account and Monte Carlo Simulation (MC) using 50.000 samples was used to compensate

for the non-linearity of the problem and provide a more accurate result. As it can be seen

from the results for one of the FPSOs analysed in (Fig. 9.22) and (Fig. 9.23) vary quite

significantly and show not to follow the mathematical trend of the corrosion model as the

probability of failure curve obtained could be fitted to a 6th order polynomial for the time

variant results and a 5th order for the instantaneous and a 4th and 3rd order respectively for

the reliability index.


It is interesting to compare the results obtained with available reliability indices published in

the available literature, as summarised in (Table 9.5) for FPSO structures and (Table 9.6)

for Tanker structures. It should be noted that in the majority of the literature reviewed no

thermal effects are taken into account and in the majority of the results published, no

corrosion effects are taken into account. The reliability indices are in certain cases annual

and in other cases for a 20 year period, a fact that needs to be taken into account when

comparing the results obtained during this study with the available published literature. The

large variability in the results both from this study and the available literature suggest that

still a large amount of work is required before commonly acceptable levels of safety can be

set for the design of marine structures using reliability based approach.

The reliability concept encompasses a wide range of probabilistic thinking and analysis. It is

able to incorporate knowledge of the probabilistic aspects of design and loading, including a

factor expressing the designer's confidence in the quality of the probabilistic information. It

can accommodate empirically determined values where probabilities are not clearly known,

and it can even take into account aspects of a shipping operation that have no bearing on

strength such as the decision made by an owner to select a probability of success from all

causes, factoring in probabilities such as disastrous events as fires and collisions. In the pure

Moatsos, I. 2005


sense, however, structural reliability starts with a goal of reaching a sufficiently small

probability of structural failure, all other types of failure aside. Of course the quality of a

structural design depends entirely on the information going into the reliability analysis, and

the approach can produce in the most sophisticated way a "perfectly terrible" design. The

old saying about computers is equally valid for a reliability analysis: "garbage in, garbage

out".

The use of probabilistic methods in design can provide several benefits and some unique

features. As bullet points among those benefits which have already been discussed in

previous chapters of this thesis include:

• The explicit consideration and evaluation of uncertainties associated with the design

variables.

• The inclusion of all available relevant information in the design process.

• The provision of a framework of sensitivity measures.

• The provision of a means of decomposition of global safety of a structure into partial

safety factor associated with individual design variables.

• The provision of a means for achieving uniformity of safety within a given class of

structures (or specified non-uniformity).

• Minimum ambiguity when updating design criteria.

• The provision of a means to weigh variables in terms of their significance.

• The provision of a rationale for data gathering.

• The provision of guidance in novel design.

• The provision of the potential for reducing weight without loss of reliability, or the

improvement of reliability with an increase in weight. Structural reliability methods

can identify and correct overly and unduly conservative designs.

In addition to the aforementioned benefits, reliability technology lends itself for certain use

for which it is much more suitable than traditional design methods. Its use includes:

• The possibility of comparison of alternative designs, particularly in the early design

stages when several competing design concepts are considered.

• The ability to perform failure analysis of a component or system.

Moatsos, I.2005


• The development of a strategy for design and maintenance of structures which age

as a result of corrosion and fatigue and to determine inspection intervals.

• The ability to execute 'economic value analysis' or 'risk based economics' to

provide a design with minimum life cycle costs.

• The ability to develop a strategy for design, warranties, spare-part requirements

• In general, as a design tool to manage uncertainty in engineering problems.

The use and implementation of probabilistic methods are not without problems. Some of the

drawbacks include:

• The use of reliability analysis in safety and design processes requires more

information on the environment, loads and the properties and characteristics of the

structure than typical deterministic analyses. Often some information might no~ be

readily available or may require considerable time and effort to collect. Time and

schedule restrictions on design are usually limiting factors on the use of such

methods.

• The application of probabilistic and reliability methods usually requires some

familiarity of basic concepts in probability, reliability and statistics. Practitioners

and designers are gaining such familiarity through seminars, symposia, and special

courses. Educational institutions are also requiring more probability and statistics

courses to be taken by students at the graduate and undergraduate levels. This

however is a slow process that will take some time to produce the necessary

'infrastructure' for a routine use of reliability and probabilistic methods in design.

• On a more technical aspect, reliability analysis does not deliver what it initially

promised, that is a true measure of the reliability of a structure by a 'true and actual'

probability of failure. Instead what it delivered is 'notional probabilities' failure and

safety indices which are good only as comparative measure. Only notional values

are delivered because of the many assumptions and approximations made in the

analysis producing such probabilities and indices. These approximations,

deficiencies and assumptions, however are made, can be found not only in

probability-based design, but also in traditional design. Approximations are made in

Moatsos, I. 2005


the determination of loads using hydrodynamics theory and in the structural analysis

and response to the applied loads. When all such assumptions and deficiencies are

removed from the design analysis, the resulting probabilities of failure will approach

the 'true' probabilities.

In using such an approach the designer also begins to enter into areas of moral and political

implications. The question arises of who will decide what the probability of failure should

be, of whether the public will understand that it never can be reduced to zero and that there

is an ever-increasing cost associated with each little reduction of risk? Casualty statistics

will give an indication of what society has traditionally accepted in structural failure rates

for vessels, but once a number is assigned to the probability of failure, there will be

tremendous pressure to make it lower from various interested and affected parties. To add

the previous questions, even more questions arise such as what protection can be afforded

and who is responsible for such decision when a ship bears out the statistical nature of the

analysis by going down, whether different types of vessels should have different structural

reliability and more importantly who is the person who decides what is the value of a

human life.

Phenomenological, modeling, prediction and physical, statistical and human factor

uncertainties will all be affected as a result of global climate changes. In case of

phenomenological uncertainties resulting from highly uncertain changes in temperature or

loading, the consequences will clearly be difficult to formulate and measure. For modeling

uncertainties the lack of availability of data in measuring the effect of extreme temperature

changes resulting from global climate change also makes it difficult to quantify the effects.

However the overall prediction uncertainties are more associated with how and when such

extreme meteorological changes might occur and not as much as with the effect they will

have on the engineering system but nevertheless their association with the entire process

should be noted. Physical and statistical uncertainties again are affected by the lack of

measurement of such type of phenomena on marine structures but the effect of climate

change could perhaps be more easily demonstrated by looking at the climate change trends.

These could perhaps be incorporated into reliability analysis by, as already discussed,

having the mean and variance of the strength, thermal stress or loading variables (depending

on how the limit state equation is formulated) themselves being random variables based on

statistical analysis of the trends encountered so far. Finally in terms of human factor

Moatsos.L 2005


uncertainties the fact that nature and the environment affect human behavior is

unquestionable. Human behavior and emotions can vary significantly depending on the

surrounding climatologically conditions thus having a direct effect on the quality of

construction and design of any engineering structure but again to demonstrate the effect of

climate change into such type of uncertainty would require additional research data and

study which falls beyond the scope of this research.

The effect of global warming on reliability analysis is hence made evident from the above.

In the absence of measured data such as variability of occurrence of extreme temperature

effects on marine structures or the measurement of temperature and thermal stresses on

ships or offshore structures the exact effect of global warming in the analysis carried out in

this thesis becomes an extremely tedious and complicated task that falls well beyond the

scope of this study but nevertheless should be pointed out as a means of perhaps linking

future research with the results, ideas and suggestions that have been documented during

this study.

Fortunately, the difficult and gloomy thoughts expressed above are just the bottom line of a

reliability analysis and issues that will eventually have to be addressed especially by

regulatory bodies and governments. At the same time, there are other benefits of reliability

analysis that can and are achieved right now such as the fact that reliability concepts can

deal with the probability of failure of structural components as wen as the overall structure.

Such an approach enables designers to make direct comparisons on the basis of overall

strength between different structural components or arrangements under different loading

conditions to evaluate their relative strengths from the perspective of a lifetime of operation.

Trade offs between strength, redundancy, and serviceability can be made to optimize

structures from the standpoint of strength, weight, cost, or any other parameter. By means of

reliability analysis, a more thorough understanding of loads, structural analysis, and

material behaviour can provide more efficient ship structures, resulting in lighter scantlings

with no reduction n the overall level of structural safety.

Moatsos,l. 2005


Chapter 9, Reference:Ang, A.H.-S., Tang, W.H. 1975, Probability Concepts in Engineering Planning and Design

Vol. I:Basic Principles, J. Wiley & Sons Ltd., New York.Ang, A.H.-S., Tang, W.H. 1984, Probability Concepts in Engineering Planning and Design

Vol. 2:Design, Risk & Relibaility, J. Wiley & Sons Ltd., New York.

Bolotin, V.V. 1981, "Wahrscheinlichkeitsmethoden zur Berechnung von Konstruktionen",VEB Verlagfur Bauwesen, Berlin (in German).

Breitung, K. 1984, "Assymptotic Approximations for Multinormal Integrals", Journal ofEngineering Mechanics Division of American Society of Civil Engineers, No. 110(3), pp357-366.

Breitung, K. 1989, "Probability Approximations by Loglikelihood Maximization", Seminarfur Angewandte Stochastik, Institute fur Statistic and Wissenschaftstheoric, Seric StoNr.6, University of Munich, Munich ,Germany.

Cassela, G., Dogliani, M., Guedes Soares, C. 1996, "Reliability Based design of the PrimaryStructure of Oil Tankers", Proceedings of the International Offshore Mechanics andArctic Engineering Symposium (OMAE 96), Vol. 2, pp 217-224.

Cassela, G., Dogliani, M., Guedes Soares, C. 1997, "Reliability Based design of the PrimaryStructure of Oil Tankers", Journal of Offshore Mechanics and Arctic Engineering, Vol.119, pp 263-269.

Casela, G., Rizzuto, E. 1998, "Second-level Reliability Analysis of a Double Hull OilTanker", Marine Structures, Vol. 11(9), pp 373-399.

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Der Kiureghian, A., Lin, H.Z., Hwang, S.P. 1987, "Second-Order ReliabilityApproximations", Journal of Engineering Mechanics Division of American Society ofCivil Engineers, No. 113(8), pp 1208-1225.

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Moatsos, I. 2005


Appendix 9, Figures

f:;(s)

fsilsr) .

o

G < 0 : Failuredomain D

Figure 9.1 Two random variable joint density function/Rs(r,s), marginal density functions/R and/s andfailure domain D.

Figure 9.2 Basic R-S problem: FRC)/sO representation.

Load effect- Se.g. bending moment

Resistance'- Re.g. flexural capacity

Failuredensity

FJI,xJ!ix)

Figure 9.3 Basic R-S problem: fHO/SO representation.

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s·

Failure State

B

Safe StateFigure 9.4 Hasofer-Lind reliability index: Linear performance function.

X·2

g(X} < 0

x'· (Design point)

g(X) = 0

X·1Figure 9.S Hasofer-Lind reliability index: Nonlinear performance function.

xiFigure9.6 Rackwitz Algorithm for finding ~HL'

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G2(X') = 0

s

Xl

Figure 9.7 The ordering problem in the Hasofer-Lind reliability index.

G(Y) <0

G(Y»O

Figure 9.8 Polyhedral approximation to the limit state.

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Figure 9.9 Fitting of paraboloid in rotated standard space (Der Kiureghian et al., 1987).

R•.'i

-__ .::=:--/s(s 1, .. ,.)

Tra«S(r}Typical Load Effect

Figure 9.10 Schematic time-dependent reliability problem.

Load effectS(t)

oFigure 9.11 Typical realization of random process load effect.

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Z(t) = R(t)-S(I)

Realizationof Z(t)

Figure 9.12 Realization of safety margin process Z(t) and time to failure.

Failure region. G(X)<O

b ~Figure 9.13 Out-crossing of vector process X(t).

Uniformlydistributedrandom numbers

~. 10r- ~~,

" Cumulative distributionfunction of randomvariable.

" R Ii .XI ..... ea zauon orartificial sample

o x

Figure 9.14 Inverse Transform Method for Generation of Random variates.

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_-,-------


Fe (g)

\.0+-------------------

Failure~fe

G(x) 0 I Fitted cumulativedistribution function

o

Figure 9.15 Use of fitted cumulative distribution function to estimate PI'

Reliability Index p in Sagging

5.0~--------------------------___,

'.5

4.0

2.110

2.5

2.0

2.5 12.5 22.5 27.517.57.5

CorroaJon In V.....

I • 0 De•. C. 11.7 DOll.C. 1•. 3 Dog. C. Poly. (O!leg. C.) Poly. (".7!leg. C.) Poly. (1•. 3!leg. c.d

Figure 9.17 Temperature and Corrosion Effect on P in Sagging.

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Prob of Fallur. P, In Hoggingeom.ion in V .. ,..

10 20 3025'5

1.00E~1

5.35E~1

3.521:-0\

1.41E~

Figure 9.18 Temperature and Corrosion Effect on Plio Hogging.I • 0 • 11.7 18.3 Expon. (18.3) Export. (1'.7) Expon. (0) I

Reliability Index ~ In Hogging

I • 0 e.g. C. • 11.7 o.g C. 1•.30..,. C. Poly. (00..,. C.) Poly. (11.7 Ceg. C.) Po~. (1•. 30..,. c.) ICorTo-'on In y..,..

Figure 9.19 Temperature and Corrosion Effect on pin Hogging.

2.0

5 1.5

~ TU.

~ 1.0 •-Jl •iii •'f 0.5caCl.

0.0

0

TerJ1)I!I'8tU'e Effect on PSF in Sagging

.- .--.-------------------T-----------T

---------------------.'-----------.• - i.. ..

-.- Extr. Still Water BM-.- Extr. Wwe BM.... Ultimate Str. Uncertainty-T-Uncert. in Wave Load Prediction• Ultimate Strength

5 10 2015

TerJ1)eI'8lure Olange·C

Figure 9.20 Temperature effect on the Partial Safety Factors in Sagging.

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Temperature Effect on PSF in Hogging

1.05

Figure 9.21 Temperature effect on the Partial Safety Factors in Hogging.

0.01

0.001

y = -1 E-09x· + 1E-07xs - 6E-06x4 + 0.0001 x3 - 0.0012x2 + 0.0061 x - .005R' =0.9983

.. .. ..• ••.-------------------- -----------'.1.00

-.- Extr. Still Water BM• Extr. Wave BMAt. Ultimate Str. Uncertainty" Uncert. in Wave Load Prediction• Ultimate Strength

30

y = 8E-10xs + 1E-09x' - 6E-07x3 + 1E-05x2 - 7E-05x + 0.0008 __ RJIy. (lirre VariantR' = 0.9944 FFSClJ)

RlIy. ( hstantaneousFFSClJ)0.0001 L_ L- ~ ~

... 0.95

~LL 0.90

fIII 0.85

iii .. ..1: 0.80iiiCl.

0.75

•0.70 ••

0 5 10 15 20

Temperature Change QC

Propability of Failure Against Corrosion Time

o 5 10 15 20 25

Figure 9.22 Instantaneous and Time Variant Probability of Failure.

/~

r-~

.-=--- ~ ---Tirre Variant FFSClJ

~ / --- nstantaneous FFSClJ

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Time (Years)


3.1

2.9

2.7

I2.5

.~j 2.3;!

2.1

1.9

1.7

1.50

Reliability Index against Corrosion TIme

3.3

y = 2E-05x'· O.OOlx2+O.OO19x + 3.1408/ A'=O.9927

~'-----~

-lirre Variant FFSa>

- nstantaneous FFSa>

RlIy. (nstantaneous FPSCb)

- RlIy. (TIITBVariant FFSa»

y = 1E-05X<. 0.0008x3 + 0.0171 x2 • 0.194x + 3.2053A' =0.9988

5 10 15

Time (Years)

25 3020

Figure 9.23 Instantaneous and Time Variant Reliability Index.

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Appendix 9, Tables

Level Calculation Probability Limit State Uncertainty Result

Methods Distributions Functions Data

I :Code Level (Calibration to Not used Linear Arbitrary factors Partial factors

Methods existing code functions

rules using (usually)

Level2 or 3)

2:'Second Second Normal Linear, or May be included 'Nominal' failure

Moment' Moment distributions approximated as second probability PJN

Methods Algebra only as linear moment data

3:'Exact' Transformation Related to Linear, or May be included Failure probability PI

Methods equivalent approximated as random

Normal as linear variables

distributions

Numerical Fully used Any form

Integration and

Simulation

4:Decision Any of the above, plus economic data Minimum cost, or

Methods maximum benefit

Table 9.1 Reliability levels and methodology.

Random Variables Distribution COYPlate thickness Normal 0.05Yield strength Normal 0.10

Young's modulus Log-normal 0.03Table 9.2 Random variables related to inherent uncertainties in strength.

Random Variables Distribution Mean COVXu Normal 1.0 0.10

Xsw Normal 1.0 0.05

X... Normal 0.9 0.15Table 9.3 Random variables related to model uncertainties.

Moatsos, I. 2()()5


Variable Distribution COV Mean

Au Ultimate Strength Uncertainty Normal 0.10 1

Mu Ultimate Strength LogNormal 0.10 Calc.

Mse Most Probable Extreme Still Water Gumbel Extreme 0.15 Calc.Bending Moment,. Load Combination Factor Constant N/A 0.78

A.. Uncertainty in Wave Load Prediction Constant N/A 0.1

Xnat Non-Linear Effects Constant N/A 1.2 S0.8 H

M_ Extreme Vertical Wave Bending Gumbel Extreme 0.15 Calc.Moment

Table 9.4 Stochastic Model Used for Time Variant and Time-Invariant Reliablity Analysis.

Reference Year Ship Type Component/Hull Analysis Reference ReliabilityGirder Method Time Index p

Frieze et al. 1991 FPS Deck Buckling FORM 6.5Method 2

1 3.520 2.8100 2.5

Hull Girder, Method FORM 1 cycle 5.9/6.9/6.61/2/3

1 3.8/4.1/3.520 3.3/3.6/2.8100 3.0/3.3/2.4

DNV 1992 FPS Deck Buckling 1 3.7Shi & 1993 FPS Hull Girder FORM 20 3.2

FriezeHull Girder w/cc FORM+ 1.5Hull Girder w/o cc FORM+ 0.3

Sun & Bai 2000 FPS Hull Girder MC 1 2.720 2.5

MC+ 1 2.120 1.922++

I Linear 2 Empirical 3 Analytical w/cc: with corrosion w/occ: + Time variant ++Fatigue

Approach Approach Approach control without structure crackingcorrosion accounting for occurring in thecontrol corrosion 21" ~ear

Table 9.5 FPSO Reliability Levels Published since 1990.

Moatsos, I.2005


Reference Year Ship Type Component/Hull Analysis Reference ReliabilityGirder Method Time Index p

Shi 1992 Tanker Hull Girder FORM 1 4.220 3.2

FORM+ 1 3.720 0.55

Chen et al. 1993 DH Tanker First Yield FORM 20 3.4Shear Side Shell 3.5Shear Inner Shell 1.9Hull Girder 2.0

Mansour & 1994 Tanker Hull Girder 20 1.5HovemMansour & 1995 DH Tanker Deck Buckling FORM 20 2.8WirschingCasella et 1996 Tanker Hull Girder 1 2.9al.Leheta & 1997 Tanker Deck Buckling FORM 20 2.2MansourWirsching 1997 Tanker Hull Girder FORM+ 1 2.8et al.

Typical Corrosion 20 2.6RateHull Girder 1 2.82xTypicai Corrosion 20 2.3Rate

Casella et 1997 DH Tanker Hull Girder FORM 1 2.7al.

Tanker Hull Girder 3.4Mansour et 1997 DH Tanker Deck Buckling 0.04al.

Hull Girder 0.8Casella & 1998 DH Tanker Hull Girder FORM 1 3.3RizzutoPaik et al. 1998 DH Tanker Hull Girder (Hog) SORM+ 1 2.6

w/cc 20 1.6°1l.9·Hull Girder (Sag) 1 2.2w/cc 20 1.1°11.5·

Guedes 2000 Tanker Hull Girder FORM 1 2.3Soares &TexeiraILinear 2 Empirical 3 Analytical w/cc: with corrosion wlo cc: + Time variant ++FatigueApproach Approach Approach control without structure cracking

corrosion accounting for occurring in thecontrol corrosion 21" year

OCorrosion • Corrosionstarts 5 years starts 10 yearsfrom the time from the timeof new- of new-huildin buildin

Table 9.6 Tanker Reliability Levels Published since 1990

Moatsos, I. 2005

CHAPTERIO

DISCUSSION & CONCLUSION

10.1 Introduction

A number of changes in ship design have been implemented over the years with the result

that in modem design longitudinal strength requirements can now be met using less material

than in older ships. One example of this relates to the introduction of segregated ballast

requirements in tankers where changes in structural arrangement have produced a new

generation of ships with length to depth ratio less than traditionally used. In providing less

material to generate the required modulus, local strength requirements become more

difficult to satisfy and the distribution of material between the plate and stiffener

components becomes critical. In this respect ultimate strength techniques such as the ones

compared and developed in this study can assist in the determinant of structurally efficient

hull cross sections. In developing the design of such sections, it should be clearly be a

primary requirement that the margins of safety against hull failure in hogging and sagging

should be similar.

This chapter discusses & concludes more in detail all the parts of this study that the author

believed were of importance. Theoretical models used throughout this study were discussed

at the end of each chapter along with assumptions made and possible implications of both

the assumption and the results. Proposals are also made on future research and experimental

procedures that would complement this study and further advance the knowledge gained in

the particular fields by future readers of this thesis and researchers studying in similar fields.

Each element of this study discussed in each of the chapters of this thesis is treated

separately but in some cases where there is a certain amount of overlap in the effects of

certain approaches taken or in the implications that certain results might have, these are

discussed together.

10.2 Thermal Stresses on Marine Structures

Thermal stress analysis and the study on the effects of diurnal temperate stresses on marine

structures formed one of the most important elements of this study. It was identified during

the critical review of published work in (Chapter 3) of this thesis that although the problem

Moatsos, I. 2005

Chapter 10.Discussion and Conclusions 401

of thermal stresses affecting marine structures troubled researchers in the mid 1950s and

1960s, and although the significant effect and even the possibility of being responsible for

structural failure was documented, very little research on the particular subjected has been

published since then.

Looking at the problem from the global warming point of view, as discussed in (Chapter 2),

the increase in average temperatures globally and the extreme nature of the weather that

countries worldwide are currently experiencing, various engineering fields such as the

automotive and the civil engineering have started looking at these effects more in detail.

With so much interest in global warming and its effects in the recent years, it surprising that

the marine technology research, design and construction communities have not started

taking into account the effects of global climate change more explicitly in their design

approaches. It could be that the nature of the industry is so conservative that unfortunately

such effects might take years yet to become normal practice and could require a catastrophic

failure or accident that would be solely attributed to such conditions, before such effects are

effectively implemented into standard engineering practices and ship structural design.

In thermal analysis of structures, temperature difference is the most important factor. In the

case of a ship's structure, as a result of the structure's size and complexity a large number of

such temperature differences can occur that can also vary between different parts of the

ship. A set of temperature conditions that can give rise to a significant temperature

difference in one segment of the ship's structure may not necessarily be the same set of

temperature conditions that will create the most adverse temperature difference for another

segment of the vessel.

Jasper's theory has a number of assumptions that require attention and are worthy of some

discussion. Although the theory neglects the effects of transverse restraint on the

longitudinal stresses, good agreement has been shown between theoretical calculations and

experimental results on both model and full scale. Away from transverse bulkheads it

appears the transverse restraint is small and the theory is satisfactory for the longitudinal

strength problem.

An interesting point arises in all theoretical approaches suggested that solutions for the

thermal stress problems for holes in plates under various boundary conditions all indicate

Moatsos, I. 2005

Chapter lu.Discussion and Conclusions 402

stress concentrations of the same order as under tensile loading conditions so that the two

effects may well be superimposed in cases where there is a temperature gradient over the

stress raiser as well as tensile stresses in operation. This would explain the cracks that have

been observed around piping holes and other stress raisers in refrigerated ships and

emphasises the importance of detail design when the detail itself is subject to a temperature

gradient.

The preliminary analysis of the FPSO structure as described in (Chapter 5) of the thesis

indicated a significant effect. Hogging ultimate strength change results compared to results

that did not include temperature effects produced a change ranging from 2.6% to 5.1% for

the temperature changes examined with the corresponding change for the average diurnal

overall change in temperature found to be 2.6%. In the case of sagging ultimate strength

change the results obtained were of the magnitude expected showing a 41% reduction in

ultimate strength during sagging in the "worst case scenario" analysed. The sagging analysis

produced a change ranging from 24.3% to 40.8% for the temperature changes examined

with the corresponding change for the average diurnal overall change in temperature found

to be 24.3%. This shows the significant effect that temperature change induced stresses

could have on the ultimate strength of ship structures. Looking at the reasons behind such

data and for an interpretation of the results obtained, some interesting conclusions can be

reached. The rapid reduction of the deck strength, which is the primary load bearing part of

the ships' structure in hogging and sagging conditions, translates to a significant reduction

in hull girder US, as it is of primary importance in all mathematical formulation used. From

a physical point of view the reduction would be more obvious when the structural

components were not in tension (as they would be in a hogging condition) when the load

bearing properties of the stiffened panel would be influenced more by properties of the

material, but rather in compression (as they would be in a sagging condition) where the

dimensions of the stiffened panel and the structural configuration of the area along with the

type of stresses imposed on the structure would be of more significance. Its is difficult to

say what effect the structural configuration of each of the vessel can have on the US as more

detailed analysis would have to be carried out (FEA for each of the vessels) in conjunction

with detailed data on the temperatures of cargo their· variation and distribution.

Unfortunately such type of data was not easy to obtain for this study as it is often that no

records are kept for analysis by FPSO owners and operators. Should such type of data, to

the level of detail and accuracy required, have been available, it would have enabled such a

Moatsos, I. 2005


study of thermal loading induced by the cargo to be made, its patterns to be investigated and

would have complemented the current work by improving the quality of the results enabling

further investigations on such effects to be carried out.

The effect of temperature change and corrosion in the reliability based structural design of

TankerlFPSO structures was investigated and a procedure was proposed which took into

account diurnal changes of temperature in the North Sea and a statistically derived corrosion

wastage mathematical model. The significant reduction of the hull girder ultimate strength

when thermal stresses and corrosion were taken into account could be attributed to the way

in which thermal stress occurrence was modelled and the extreme nature of the values used

which in our case had a 20-year period. Extreme diurnal temperature variations occurred in

summer months during which extreme wave bending phenomena would have a lower

probability of occurrence, which explains the magnitude of the results. Unfortunately no

new evidences from experiments and design practices exist to justify the importance of

thermal effects on ship structures, but it is the observed and well documented abnormal

changes in surface temperature and global weather and the fact that marine structures

experience abnormal weather phenomena more often than they did in the past that justify

the need for more research in the field. One could also argue that temperature change at a

specified site is a random variable, which could be fitted by a certain probabilistic

distribution based on the loading and offloading manual of the FPSO under typical loading

conditions, hence overestimating the effect of temperature change. This would be true but it

would only enable modelling of temperature change for the cargo areas of the structure and

not the diurnal temperature change which is more significant. More research in developing

accurate temperature models is certainly required.

The size of stresses measured indicates the importance of this problem in the design of the

hull girder. It reinforces the argument for maintaining low still water loading stresses where

the temperature stress can vary between tensile and compressive values during the course of

voyage or time subjected to loading which will be the case in all ships which do not have a

large amount of internal heating or cooling. In the latter cases it is possible that no matter

what the air and sea temperature variations are the temperature stresses will be either tensile

or compressive at certain parts of the hull girder and might be offset by the way the ship is

loaded. This requires further investigation of particular cases.

Moatsos, I. 2005


10.3 Ultimate strength

A framework for predicting the ultimate strength of ships for various configurations under

vertical bending moment was proposed and incorporated in a Visual Basic code for MS

Excel 2003. The code incorporates various proposed formulations which were selected for

their simplicity and ease of use when compared with high-end numerical solutions and can

be used for comparison and analysis for ship structures but is also flexible enough to accept

further approaches to be used and compared but also any corrosion wastage data as input.

The approach calculates the ultimate strength moment of the hull by integrating the assumed

stress distribution with respect to the neutral axis. This resulted in explicit ultimate moment

expressions for the sagging and hogging conditions. The simplified formulation assumed

uniform compressive stress distribution (average values), but the actual stress distribution

will be non-uniform as a result of buckling and post buckling effective width. If the uniform

value is a good indication of the actual value, then the calculated moment should not be

very different from that due to the actual stress distribution, because the distance to the

neutral axis is the same in both cases. As the emphasis of the approach is to use simple

formulation, uniform (average) compressive stress is assumed.

As far as the developed code that formed the core part of the MUSACT code is concerned

and the theory behind this approach the bending moment sustained by the cross section is

obtained from the summation of the moments of the forces in the individual elements and

the derived set of values defines the desired moment-curvature relation. Initially the position

of the neutral axis is required and is estimated through an elastic analysis because, when the

curvature is small, the section behaves elastically. However, the approach creates two

distinct problems in its implementation:

3. The sequence and spacing of the imposed curvatures strongly influences the

convergence of the method due to the shift of the neutral axis.

4. Modelling the ship's section and determining the position of the neutral axis itself

are important issues.

5. Although Faulkner's method used for the determinant of the ultimate strength of the

stiffened panels in comparison with all other available methods produces the best

Moatsos, l. 2005


results, it gives poor prediction when the initial imperfection (including residual

stress in plate, initial deflection in stiffener and load eccentricity) is large.

The procedure used in this work to predict the behaviour of the hull girder under

predominant longitudinal bending seems to be quite accurate when the results are compared

with those obtained with different approaches, but also when applied to already built FPSO

structures, both new-built and conversions. On the other hand, if the preparation time of the

model and the computational running time are considered and compared with methods

using finite-elements or ISUM elements, then the developed procedure and code is far better

and more useful for design practice. The code takes about 3-5 minutes to run (depending on

the complexity of the structure) using a Pentium 4 2.8GHz Personal Computer, simulating

corrosion and thermal effects and calculating the US of both panels and overall hull girder

in sagging and hogging conditions using a variety of formulations, while finite-element

methods normally need a parallel computing environment and may take from several hours

to several days (always depending on the complexity of the problem) to provide a result that

needs to be interpreted according to the boundary and modelling conditions used. In relation

to the preparation time of the model, finite-element approaches may take several weeks to

implement the model (for a relatively experienced user of the FE code used) not to mention

the time required to familiarise the person performing the analysis with the software and the

code in order for accurate and realistic results to be acquired. On the other hand the code

developed only requires a couple of days for familiarisation, implementation and

interpretation of the results obtained. It has to be noted though that the code runs in an MS

Excel environment and is not a stand-alone program and hence the user has to be in

possession of a version of MS Excel in order to run the code and obtain results.

Furthermore the approach predicts a load-shedding pattern in the behaviour of the stiffened

plate after buckling. This prediction is based mainly on the assumed variation of the

effective width of the associated plate and thus it requires confirmation by other methods,

experiments and finite-element approaches. This confirmation is especially important for

the prediction of the ultimate strength of the ship hull girder by taking into account the cross

section due to the different state of strain of each stiffened element where some of them are

already in the pos-buckling region. As far as residual stresses are concerned and their

impact in plate elements used in this analysis, a particular case of stress distribution was

assumed as specified and formulated in the theories and approaches used. However a

Moatsos, I. 2005


smooth transition between the tension and compression zones may easily be implemented

by the modification of the equations used, quantifying the changes of the material

behaviour.

As stated in the introduction of this chapter, ultimate strength techniques such as the ones

compared and developed in this study can assist in the determination of structurally efficient

hull cross sections. In developing the design of such sections, it should be clearly be a

primary requirement that the margins of safety against hull failure in hogging and sagging

should be similar. This requires that the buckling and post-buckling properties of the upper

and lower parts of the structure should be properly matched to the applied bending moments

in sagging and hogging respectively. Load shedding characteristics of panels beyond initial

buckling can evidently be of critical importance, and the relative merits in this respect of,

for example, flat bar, tee-bar or bulb plate longitudinal stiffeners must be considered.

At the level of detailed design of compression panels, it is tempting to argue that the most

efficient design will be one in which the various modes of instability, whether by stiffener

tripping, web buckling, plate buckling or overall panel column instability, should occur at

similar levels of stress. This approach to design optimisation, sometimes referred to as the

"one-hess shay" concept, has often been used in the past in other structural contexts. The

analysis suggested by various approaches in the published literature confirms the possible

danger of this approach. If the simultaneous occurrence of various modes of failure leads to

a sudden, rapid deterioration in compression stiffness (a high rate of load-shedding) then

any reserve of strength beyond the limit bending moment may be reduced to zero. Not only

would there be no warning of imminent failure, but such failure could be total and

catastrophic. It is not possible on the basis of this study and from all the published literature

examined to draw any general conclusions regarding the optimum distribution of material in

hull cross-sections. It can be said though that there is clearly a need for structural designers

to use the tools now available for calculating ultimate compressive properties of stiffened

panels to investigate systematically the relative merits of alternative design configurations.

The predicted moment-curvature relationship for the hull beyond its ultimate strength

conditions must be viewed as approximate, particularly at the higher levels of curvature

where a number of assumptions made could be violated such as:

Moatsos, I. 2005


• The stabilising effect of displacement continuity between elements ignored in the

analysis may become significant at high levels of strain.

• At high strains, the assumption that plane sections remain plane is likely to be

violated as will the assumption of circular bending.

The sudden change of slope of the moment curvature diagram in sagging, and the steep

negative slope resulting from rapid load shedding both in the results obtained by the

MUSACT code and LRPASS, suggest that failure of such a hull in sagging would be

sudden, rapid and potentially catastrophic. Although behaviour beyond the ultimate is of

theoretical interest, the ability to predict maximum strength is crucial in the assessment of

ship safety. Such predictions are quite sensitive to assumptions regarding corrosion, so a

logical and consistent approach is needed to specify the margins to be used in strength

calculations. The results presented are also inconclusive regarding the possible influence of

imperfections due to fabrication, as it was not intended to investigate the effect in the first

place but nevertheless they influence the accuracy and behaviour and failure patterns of

stiffened panels and should be investigated more in detail in future research.

Using results from large-scale box girder models, a 113 scale frigate hull model, a

commercial widely used code and numerical results available in the published literature, a

comparison was made of the approaches used and the code developed. The results of the

comparisons with experiments and numerical evaluations show that any simplifications and

assumptions made were acceptable and did not compromise the accuracy of the final results.

With the Triton being the only conversion-built FPSO and the only structure with a double

bottom and Schiehallion and Anasuria only having a single bottom and being purpose-built

FPSOs, the comparative results allow us to make a number of interesting conclusions:

• The overall structural strength of the FPSOs is greatly benefited from a double

bottom, as the double bottom FPSO has a significantly larger ultimate bending

moment in both sagging and hogging conditions.

• The two purpose built FPSOs although of relatively similar size and structural

configuration, exhibit different overall ultimate bending moment behaviour,

resulting from the structural details and the materials used throughout the structure.

Moatsos, I.2005

Chapter IO.Discussion and Conclusions 408

• Although the double bottomed FPSO demonstrates significantly higher ultimate

bending moments when compared with the single bottomed FPSOs, in the sagging

condition, the loss of strength is far more rapid with progressively increased applied

curvature. This is obviously subject to the post ultimate strength being modelled

accurately and there is still a significant amount of research & progress yet to be

made on this subject.

Overall some final conclusions and additional suggestions can also be made:

• The ultimate collapse strength of a ship's hull under a vertical bending moment

correlates with the failure of the side shells as well as of the compression/tension

flanges and is a significant measure of the ship's hull strength and should be used in

design and in the assessment of ship strength and/or reliability.

• Predictions of Mu appears feasible within acceptable confidence limits, using the

various approaches discussed but there are significant differences in the ultimate

moment results obtained from the different formulas and approaches used in the

companson.

• In design, the rules of classification societies specifying the requirements for the

ship section modulus should be based on ultimate strength rather than initial yield,

as in some cases initial yield does not reflect the true strength of the hull girder.

• All proposed approaches and the entire framework provide quite reasonable results

in comparison with experimental data and numerical results. As the approach takes

into account the geometric and material properties of the hull section more precisely,

it may be applied to any general-type hull cross section. The framework and code

developed may be useful in preliminary design estimates of the ultimate strength of

ships under a vertical bending moment.

• Inclusion of tripping formulation in the behaviour of stiffened panels is seen to be

very important. The deck stiffeners, made of bars, don't have much flexural-

torsional rigidity and the calculated tripping stress is lower than the flexural

buckling stress of the stiffener with associated plate. This fact leads to a very high

reduction of the ultimate bending moment in sagging compared with the moment in

hogging, where the deck is in tension. Future work is required on the subject and, as

it can be seen from the relevant literature nowadays it is possible and relatively easy

Moatsos, I. 2005


to compare the prediction of the tripping stress using approximate methods and

results of finite-element methods for stiffened panels.

10.4 Corrosion Modeling

Reliability assessment by considering corrosion and fatigue is very important for the

optimal scheme of maintenance and repair. Different corrosion models would have

significant influence on the assessed reliability and by studying some of the currently

available corrosion models it is argued that not all of these models may fully reflect the

reality. The models adopted in addition to being a more flexible alternative to all other

suggested also generalise the concept by including an early phase with the corrosion

protected surface and free parameters that can be adjusted to the data in specific situations.

Residual stresses and corrosion have a degrading effect on the ultimate moment. However,

these effects occur at separate times in the ship's life; the residual stresses are present in the

early stage of the ship's life and the effect tends to reduce with the normal operating

conditions, while the corrosion level tends to increase with time. So both effects should not

be considered together for design purposes, i.e., if an allowance for corrosion is included in

the design, then a reduced allowance for the residual stresses should be considered.

The corrosion model used does not explicitly take into account the effect of pitting and

rather an overall wastage of the members approach is used which can limit the modelling of

the actual corrosion process encountered. Nevertheless when compared with a linear

approach the non-linearity of the physical problem is modelled significantly better as it can

be seen from the detailed description of the process. For the calculation of the ultimate

strength of the entire hull girder the approach is very much dependent on the accuracy of the

corrosion model and the maximum wastage used. For the time dependent nature of the

corrosion process to be model accurately, one has to take into account the time dependent

nature of the variables into account and calculate the probabilities of failure using an

approach that will be able to interpret accurately the non-linearity of the problem.

In the corrosion models for the 2 approaches in the MUSACT code, in all cases, no repairs

are assumed and it is assumed that for the first 5 years of the vessel's life there is no break-

down in the CPS after which corrosion follows each of the models for a total of 30 years

Moatsos, I. 2005

Chapter lO.Discussion and Conclusions 410

assuming that no repairs are carried out on the structure. The nature of operations for FPSO

structures restrict frequent repairs in the cargo and ballast holds. Significant repairs can only

be effectively carried out when the FPSO ceases operations, to an obvious financial loss,

and severs and abandons the field that is currently assigned to. This certainly does not

negate the fact that repairs would often be carried out on the structure as a results of period

surveys where defective plating and structural members would be replaced. As a result of

such conditions, the assumption made appears to be a relatively good representation of the

actual condition the structure might be throughout its operational life. Looking at the two

corrosion modelling approaches it is interesting to note that both produce very similar

results after 30 years of corrosion, a fact that occurs from the maximum wastage used in

each of the approaches being similar, but throughout the life of the vessel the amount of

corrosion wastage that each of the approaches calculates, varies with the linear model

underestimating the values by as much as 2 times compared with the non-linear approach.

Hence it was decided to proceed to reliability analysis by using the non-linear approach and

avoid the conservative linear method that would oversimplify the mathematical modelling

of the phenomenon and add more assumptions and simplifications to this analysis.

When combined with the different US formulation, the results can vary with the US results

following the "trends" and shape curves of the corrosion models used demonstrating that the

corrosion model to be chosen will influence greatly both the strength and reliability results

to be obtained. As it can be seen from for Anasuria the difference is in the range of 3.4% for

the OB, 7.5% for SS, 3.1% for the Deck, 2% for Sagging US and 1.5% for Hogging US for

no corrosion between the Paik simplified formulation plate US approach and the author

developed analytical approach with the Paik approach providing more conservative results.

10.5 Load Effects Modelling

Applying the lACS formulation described in (Section 8.8) of this chapter to the 3 FPSO

structures provided the minimum design midship still-water bending moment values and the

minimum design midship wave-induced bending moments as summarised in (Table 10.5).

After comparing the strength results obtained with the lACS loading levels specified (lACS,

1989), (lACS 2003) it can be seen that the safety factors obtained when combined with the

still water loads calculated are rather low. Such low values of safety factors and especially

the pronounced influence of the wave component on their values, underlines the need to

Moatsos, I. 2005

Chapter lO.Discussion and Conclusions 411

make the predictions of the loads on, and the strengths of, hull structures as accurate as

possible. It is doubtful if, even in the light of improved knowledge and understanding of the

phenomena involved, factors as low as these calculated should be accepted. The adverse

effect of corrosion, and the need to control or monitor it has been evident in throughout this

entire thesis and is particular evident from this comparison.

Using commonly applicable deterministic load combination methods, it was determined that

the peak coincidence as applied in the existing ship rules is very conservative. On the other

hand, other deterministic methods including Turkstra's rule and the SRSS rule, all

underestimate the combined bending moment, with the SRSS rule being the least

satisfactory. Using stochastic methods, including the exact point-crossing method,

approximate load coincidence method and the Ferry Borges method, all lead to identical

predictions. For code application, load combination factors are introduced to reduce the

conservatism inherent in the existing ship rules. A considerable reduction of the total design

bending moment, as required in the existing ship rules, is found to be acceptable. It should

also be noted that the load combination factors are dependent on the type of distributions for

both SWBM and VWBM, the specified design SBWM and VWBM, as well as the reference

time period. The load combination factors presented in this paper are valid for the particular

FPSOs analysed and no attempt whatsoever should be made to consider these in amore

general fashion for other types of vessels.

The extreme models used for the calculation of loading are only dependent on the number

of occurrences and not on the total time spent in that condition. One interpretation of this

could be that the uncertainty is associated with changes in the loading, and not with the

duration of the condition. This is a suitable assumption for merchant ships, where the same

loading conditions are maintained over the whole duration of the voyage. The assumption

might not hold for an FPSO, which experiences continually changing loading every day,

where higher uncertainties would be expected. On the other hand, FPSOs are generally

fitted with better loading monitoring instruments than traditional tankers, resulting in better

load control and thus reducing the uncertainties in the effective calculation of the SWBM.

All these points were considered when assigning uncertainties to the SWBM in the extreme

and stochastic model for reliability analysis. Furthermore from the operational profile of

the vessels is such that they will be experiencing, almost always hogging still water bending

moment and the extreme SWBM values for the ballast load condition will tend to be

Moatsos, I. 2005

Chapter l O.Discussion and Conclusions 412

conservative as a result of the distributions used during the analysis being the same for

hogging and sagging conditions and not taking into account the effect of heavy weather

countermeasures during this study.

Short term responses in irregular waves were calculated usmg the principle of linear

superposition and wave statistics. The short term responses were combined with long term-

wave statistics for the specific area of operations of the FPSOs in order for the long-term

distribution of the VWBM to be determined. When the long-term distribution is known, the

most probable extreme value in any reference period may be found. The reference period

can be 1 or 20 years for the reliability analysis. During the long-term response analysis

carried out, it was stated in (Chapter 8) that the particular area wave statistics were believed

to give a good representation of the actual operational location of the FPSOs analysed.

Different fields may have different wave statistics, which may lead to variations in the wave

induced loads acting on the vessel. The recent trend in offshore development is to develop

marginal oil fields, with shorter field life and lower field value. Under such circumstances,

it may be desirable to design the FPSO with a longer service life and then operate the vessel

at new locations after a field is depleted. If this is the case, thorough consideration during

the design procedure should be given to where the vessel may be operated in its lifetime.

Getting the design right the first time may save costly improvement at a later stage.

It was evident during the analysis that the largest VBM response was generated when the

wave direction is predominately head-on or from the stem. It is obvious that this difference

in response to waves from different angles will affect the overall probabilities of

exceedance, depending on the vessel's heading. It is assumed that traditional tankers have

equal probability of encountering waves at all headings during a voyage, as opposed to

FPSOs, where the waves will have higher probabilities of approaching the vessel from

certain angles. It is important to keep in mind that by wave direction, we define the

predominant direction of the waves in the sea-state, relative to the ship heading. Although

the wave direction could be O', waves will approach from other directions at the same time.

This "short-crestedness" was achieved in the theory behind our analysis and used during

this study by introducing the spreading function, as described in (Chapter 8). The largest

amplitudes of responses were found at 180° and 0° which represent following seas and head

seas respectively. The lowest response was found at 90°, when the vessel encounters the

waves sideways. These results are quite reasonable and in good agreement with results

Moatsos, I. zoos

Chapter l O.Discussion and Conclusions 413

obtained from various other similar analyses found in the published literature. The

magnitude of the maximum response is approximately 500MNm.

During the slamming analysis of this study, for the still water loads, DNV Rules and lACS

suggested formulation were used to determine the maximum values to be used for the

combination of loads and the Jensen and Mansour approach using code developed for the

calculation of the long term hogging and sagging wave bending moments. The results were

compared with the values given from the lACS Rules and the DNV modified Rules with a

Sagging to Hogging ratio of 1.41, 1.45 and 1.35 respectively, Sagging to lACS Rule ratio of

1.20, 0.93 and 1.43 respectively. According to the results the difference between the rules

and approach used is quite significant with differences of 22% between the DNV Rules and

the simplified approach and 35% between the lACS Rules in the case of one of the FPSOs

analysed and the simplified approach as a result of the draft-to-length ratio with the values

of the method being lower than the Rules computed values. As the methodology is

dependent on the area of operations of the vessels this signifies that the prescribed rule

requirements can often be inadequate in determining the maximum bending moments and

some form of adjustments would be required to compensate for the location of operations

instead of one overall approach for all locations.

Combining the vertical bending moments in an appropriate way is not a straightforward

task, given the different random nature of the loads. Still water loads are very slow varying,

wave induced loads have load frequency, whereas slamming induced high frequency loads.

All three have been considered during the analysis. These loading components have been

considered independent and the Ferry Borges-Castanheta load combination methods was

applied, after comparing all the available options, to obtain a load combination factor. As no

reliable information on the loading procedures for some the FPSOs was made available, a

simplified operation profile based on the production capacities was used, and a rectangular

pulse process was fitted to describe the nature of the loading conditions experienced. The

load combination factor was found to vary significantly with the ratio of Stillwater load to

the total load. It is also interesting to note that the load combination factors remain the same

for hogging and sagging with each loading condition. Historically several deterministic

methods have been applied to derive load combination factors for SWBM and VWBM for

both sagging and hogging conditions. The correlation between these loads is negligible for

the estimation of the extreme combined bending moment. In the existing ship rules, such as

Moatsos, I. 2005


the lACS Requirements, SWBM and VWBM are simply added together, assuming that the

maximum values of the two loads occur at the same instant during a ship's design life.

lACS also specifies that the maximum SBWM and VWBM should not exceed their

respective allowable values, even if one of the moments is negligible. As the SWBM and

VWBM are stochastic processes, the maximum SBMW and VWBM do not necessarily

occur simultaneously in a ship's service lifetime. The load combination factors were

calculated for the three loading conditions, based on the operational profile and extreme

loads and for all conditions in all events considered (different locations, different load

models etc). These calculations form part of the basis of the reliability analysis.

10.6 Time Invariant and Time Variant Reliability Analysis

The instantaneous long term reliability of the vessel was obtained using the limit state

equation described in (Chapter 9) using a FORM approach and improving the results by

using a SORM approach but without taking into account of time and computing the

probabilities of failure and reliability indices by using the values that result as most

probable extremes for the loads and for each corrosion year for the ultimate strength and

that are distributed according to the stochastic model.

During the time-invariant analysis for Anasuria FPSO, the annual reliability index in

sagging was found to be varying from 3.819 to 4.714. in the un-corroded state. As

temperature differences increased and the amount of corrosion in the structure increased as

well, a reduction in reliability indices was noticed as expected For Triton FPSO, the annual

reliability index was found to be varying between 2.359 to 2.75 in the un-corroded state.

This is rather low value corresponds to approximately one failure in 110 years or one failure

per year in 110 structures. From the reliability analysis, it is also found that the safety of the

FPSOs is very sensitive to variables associated with the wave bending moment.

For the time-variant reliability results, the variability of the variables with time was taken

into account and Monte Carlo Simulation (MC) was used to compensate for the non-

linearity of the problem and provide a more accurate result for Schiehallion FPSO. The

results vary quite significantly and show not to follow the mathematical trend of the

corrosion model as the probability of failure curve obtained could be fitted to a 6th order

Moatsos, I. 2005


polynomial for the time variant results and a 5th order for the instantaneous and a 4th and

3rd order respectively for the reliability index.

A number of assumptions have been taken into account in each of the approaches used

which also restrict the accuracy of the problem and can be found in each of the relevant

publications in detail. Since closed form solutions were used extensively throughout this

analysis, the accuracy of the results cannot be compared with those that one could obtained

by running a detailed FE model or a non-linear approach for the determination of the loads.

Nevertheless when compared in terms of time required for the calculation the closed form

approaches can quickly produce sufficiently accurate results for a designer to assess the

safety of the structure since all the methods used have been extensively compared with

model tests or they are the result of such model tests. The corrosion model used does not

explicitly take into account the effect of pitting and rather an overall wastage of the

members approach is used which can limit the modelling of the actual corrosion process

encountered. Nevertheless when compared with a linear approach the non-linearity of the

physical problem is modelled significantly better as it can be seen from the detailed

description of the process. For the calculation of the ultimate strength of the entire hull

girder the approach is very much dependent on the accuracy of the corrosion model and the

maximum wastage used. For the time dependent nature of the corrosion process to be model

accurately, one has to take into account the time dependent nature of the variables into

account and calculate the probabilities of failure using an approach that will be able to

interpret accurately the non-linearity of the problem.

It is interesting to compare the results obtained with available reliability indices published in

the available literature. It should be noted that in the majority of the literature reviewed no

thermal effects are taken into account and in the majority of the results published, no

corrosion effects are taken into account. The reliability indices are in certain cases annual

and in other cases for a 20 year period, a fact that needs to be taken into account when

comparing the results obtained during this study with the available published literature. The

large variability in the results both from this study and the available literature suggest that

still a large amount of work is required before commonly acceptable levels of safety can be

set for the design of marine structures using reliability based approach.

Moatsos, I. 2005


10.7 Future Research

From the evidence produced in this thesis and the results and comparisons with full scale

tests it is clear that thermal stresses of the same order as the still water loading will be

encountered by nearly all ships. There is a considerable demand for the carriage of cargoes

at more extreme temperatures than operators and designers are experienced at present and

the thermal stress problem is likely to increase in importance. The stress resulting from

thermal gradients can be calculated with sufficient accuracy by existing methods. such as

the on proposed in this thesis by the author, where there is no problem of stress

concentration involved. However information on the frequency and magnitude of the

thermal gradients experienced by ships in operation is insufficient for design calculations

and more research is required on:

1. Model tests for details which may give rise to stress concentrations

2. The stresses resulting from the gradients. Away from points of stress concentration

and transverse restraint these may be calculated by existing methods but theoretical

and experimental work will be required for local stresses around details which are of

most importance.

3. The fatigue properties of ship steels under steady load, fluctuating loading and the

extreme temperature gradients.

4. Methods of alleviating thermal effects due to loading, local design, use of special

material and crack arrestors, insulation, etc.

There are many other areas of ship structure temperature research worthy of consideration

even at this time. For example, the thermal buckling of curved and flat plates under

conditions of thermal input peculiar to ship structures and in conjunction with non-thermal

buckling loads is one problem that requires investigations of an analytical and experimental

nature. Thermal stresses in flat plates resulting from two-dimensional temperature gradients

and one-, two-, or three-dimensional conditions of restraint are another type of investigation

that could be undertaken. Researchers undertaking such an investigation must carefully

consider the fact that the approaches used in analytically solving these problems must

reflect rather sensitively the range of temperatures and the temperature distribution peculiar

structure and its environment. In other words, there is a chance that without knowing in

advance the temperature conditions, one can normally expect a considerable amount of

Moatsos, I. 2005


effort will be devoted to solving a completely unrealistic problem, or even a problem which

is non-existent in ship structures. One can argue that such investigations can be used to

define the limits of temperature gradients that must exist in order to influence the behaviour

of the structure. This may be necessary in the event that instrumentation of an actual ship is

not feasible. Ultimately, however, it becomes necessary to provide experimental proof using

a full-size ship. In effect, then, by conducting research involving ship structure temperature

effects without first defining the important parameters, one merely postpones the

unavoidable task of full-scale experimentation.

It is widely accepted and the author agrees that there is a lack of experimental data from

large-scale steel models, and there is a need for further verification of all published and

future developed formulation using such data. In particular, tests are needed using models of

double hulled structures as such types have never been tested and all available published

results are based on numerical studies.

Although it was not investigated in this thesis but nevertheless is an interesting feature that

the author of this thesis came across in a variety of publications that the ultimate bending

moment in the upright position is greater than the moment at small angles of heel, no matter

if the vessel is hogging or sagging. It is necessary to evaluate if this reduction should be

included in the rules for classification societies. In practice, if an Elasto-plastic analysis of

the hull girder is performed and the calculation of the minimum ultimate moment is

required. then one should look for the minimum at an angle of heel of about 10° or more.

Alternatively, a reduction to the upright moment should be considered but this would be

worse to the 10°C angle of heel proposal as the degree of the reduction depends on the

compressive strength of the deck and the side panels.

Future development of approximate methods to predict the hull girder strength could

perhaps include implementation of an explicit method that can account for transverse

strength of the hull and overall buckling of large panels. In order for this to be achieved it

would be important to test extensively over the practical range of plate and column

slenderness of the derived load-end shortening curves of unstiffened and stiffened plates,

investigating carefully the agreement in the post-buckling range. Also load-shedding

characteristics of stiffened panels after initial buckling can strongly influence the moment-

Moatsos, I.200S


curvature characteristics of a ship's hull and certainly more work is needed on this aspect of

structural behaviour.

An interesting feature in the analysis that was not examined in detail was the statistical data

used for representing the sea conditions in each area. It is certain that by using almost

similar data and such assumptions in all FPSO analyses the level of accuracy is certainly

compromised. Such decision and assumptions had to be made as a result of lack of data but

nevertheless the author believes that the data used gives a reasonable representation of what

conditions are in each of the area of operations of the FPSOs. It would be interesting to

perform a study investigating the effect of the variability of wave induced loads acting on

the vessels by using data obtained from other sites and how these compare with the

prescribed levels of safety used today. There is always a strong possibility that the particular

vessels may be required to operate even in a different continent under completely different

conditions that could affect the overall structural safety of the vessel.

The theory for time-dependent reliability assessment has developed rapidly, although in

certain aspects it is not as fully developed, researched and publicised as time independent

reliability. We can safely reach the conclusion that the simulation-based approaches become

natural extensions of time-independent analysis once the out-crossing rate can be estimated

efficiently, however, the FORMISORM methods applied to time-dependent problems to

determine probabilities of failure tend to be considerably more difficult and laborious than

for time independent problems and researchers often have to make use of numerical

techniques to solve the resulting formulations with importance sampling suggested as the

approach producing the most satisfying results). Unlike time independent reliability

techniques. for which there has been extensive discussion and comparison. there has been

rather little comparison of the various approaches for the time-dependent solution

techniques. This can be attributed to the excessive computational times required for basic

(e.g. crude Monte Carlo) comparisons when stochastic processes are involved.

For many problems of practical significance. a fully time-dependent approach is only

required when the resistance basic variables are time-dependent or when more than one

loading case must be considered. It is evident that the methods of solution which are

necessary usually are too complex for application in practical design and for use in

Moatsos, I. 2005

Chapter to.Discussion and Conclusions 419

structural design codes. For these, simplified rules are required. How such rules might be

derived is a matter of particular importance for relating design code formulations to

structural reliability and an area that still deserves and requires a large amount of research.

Overall having touched upon the way that global warming will affect the individual

variables forming the limit state equation one can see that the results will vary depending on

how extreme the loads or the corrosion might be as a result of significant temperature or

weather changes. An attempt was made in this thesis to quantify some of these effects. The

exact effect of Global Warming and global climate change forms itself an issue of larger

debate not only to the engineering research community but is tackled more widely by

medical, social and political sciences. It has nevertheless been brought often to the attention

of the media and the public extremely often as extreme climate phenomena is not just only

easily observable and affect our everyday lives but also often result in catastrophic and

tragic events that affect the lives of millions of people worldwide. One has to just look at

the recent global effect that and isolated incidents such as Tsunami's or extreme climate

changes in Africa affect and what global social, economical and political effect they not

only had but still have.

The optimistic trend of the engineering research communities examining more in detail the

effects of Global climate change proves that such phenomena do not only exist and that

their effects should be investigated more in detail but also have a direct impact on the safety

of engineering systems. Hence the effects of such phenomena on marine structures should

not be taken lightly but instead always incorporated into any design and analysis approach

used. The conservative nature of the marine industries has always been the deterrent of

promoting pro-active engineering research in such fields and in the case of the effects of

global climate change research the engineering research community should not await for a

new catastrophe to occur as a result of such conditions before researching ways of

describing the particular effects on engineering structures in a better mathematical format or

the means of designing safer structures.

Moatsos, I.2005


10.8 Closure

The study presented in this thesis constitutes the first stage in the development of a

rationalised framework for the study of the effects of thermal stresses in marine structures

from a reliability and probabilistic point of view which formed part of the research interests

of the Structures and Reliability Group in the Dept. of Naval Architecture and Marine

Engineering of the Universities of Glasgow and Strathclyde. It is hoped that the work

presented in this thesis will be useful, at least to the Structures and Reliability Group in the

Department, in pursuing further research in the analysis of marine structures.

Moatsos, I.2005

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